Interferometry system having a dynamic beam steering assembly for measuring angle and distance

ABSTRACT

The invention features an interferometry system that measures changes in the angular orientation of a measurement object and that also includes at least one dynamic beam steering assembly. The dynamic beam steering assembly redirects one or more beams within the interferometry system in response to a change in the angular orientation of the measurement object. In many embodiments, the presence of the dynamic beam steering assembly permits the interferometry system to measure the angular orientation of the measurement object using only a single measurement beam to contact the measurement object. Furthermore, in many embodiments, a control signal derived from the measurement beam contacting the measurement object causes the beam steering assembly to redirect a measurement beam to contact the measurement object at normal incidence. When at such normal incidence, the interferometry system can calculate the angular orientation of the measurement object based on one or more interferometric signals derived from the measurement beam or based on the orientation of the beam steering assembly itself.

This application is a continuation-in-part application of application Ser. No. 09/305,828, filed May 5, 1999, now abandoned.

BACKGROUND OF THE INVENTION

This invention relates to interferometers, e.g., interferometers for measuring the position and orientation of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system.

Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.

In many applications, the measurement and reference beam components that enter the interferometer have orthogonal polarizations and frequencies separated by a heterodyne, split-frequency. The split-frequency can be produced, e.g., by Zeeman splitting, by acousto-optical modulation, or by positioning a birefringent element internal to the laser. A polarizing beam splitter directs the measurement beam along a measurement path contacting a reflective measurement object (e.g., a stage mirror), directs the references beam along a reference path, and thereafter recombines the beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that passes through a polarizer that mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal at a split-frequency. When the measurement object is moving, e.g., by translating a reflective stage, the heterodyne signal is at a frequency equal to the split frequency plus a Doppler shift. The Doppler shift equals 2vp/λ, where v is the relative velocity of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, and p is the number of passes to the reference and measurement objects. Changes in the optical path length to the measurement object correspond to changes in the phase of the measured interference signal at the split-frequency of the measurement and reference beam components that enter the interferometer, with a 2π phase change substantially equal to an optical path length change nL of λ/p, where n is the average refractive index of the medium through which the light beams travel, e.g., air or vacuum, and where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object. Similarly, multiple interferometers can be used to measure changes in distance to multiple points on the measurement object, from which changes in the angular orientation of the measurement object can be determined.

Such interferometers are often crucial components of scanner systems and stepper systems used in lithography to produce integrated circuits on semiconductor wafers. The lithography systems typically include: at least one movable stage to support, orient, and fix the wafer; focusing optics used to direct a radiation beam onto the wafer; a scanner or stepper system for translating the stage relative to the exposure beam; and one or more interferometers to accurately measure changes in the position of the stage relative to the radiation beam. The interferometers enable the lithography system to precisely control which region s of the wafer are exposed to the radiation beam.

SUMMARY OF THE INVENTION

The invention features an interferometry system that measures changes in the angular orientation of a measurement object and that also includes at least one dynamic beam steering assembly. The dynamic beam steering assembly redirects one or more beams within the interferometry system in response to a change in the angular orientation of the measurement object. In many embodiments, the presence of the dynamic beam steering assembly permits the interferometry system to measure the angular orientation of the measurement object using only a single measurement beam to contact the measurement object.

Furthermore, in many embodiments, a control signal derived from the measurement beam contacting the measurement object causes the beam steering assembly to redirect a measurement beam to contact the measurement object at normal incidence. When at such normal incidence, the interferometry system can calculate the angular orientation of the measurement object based on one or more interferometric signals derived from the measurement beam or based on the orientation of the beam steering assembly itself. In addition, many of the embodiments involve optical configurations that preserve the linear polarizations of beams incident on the optics, e.g., the use of corner cube retroreflectors are minimized.

In general, in one aspect, the invention features an interferometry system including an interferometer, a control circuit, and an angle measurement system. During operation the interferometer directs a measurement beam along a measurement path contacting a measurement object and combines each of at least two portions of the measurement beam with a corresponding reference beam to form at least two overlapping pairs of exit beams. The interferometer includes a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the measurement beam to the measurement object and the measurement beam contacting the beam steering element. During operation the control circuit causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object and the angle measurement system which calculates the change in angular orientation of the measurement object based on at least one of interferometric signals derived from the overlapping pairs of exit beams and the reorientation of the beam steering element.

In some embodiments the interferometer directs the at least two portions of the measurement beam to contact the beam steering element before combining each of them with the corresponding reference beam. In other embodiments, the interferometer directs the measurement beam to contact the beam steering element a second time, after which the interferometer separates the measurement beam into the at least two portions. 39.

In further embodiments, the interferometer further includes a plurality of reflective surfaces oriented to direct the measurement beam, the portions of the measurement beam, a progenitor beam for the reference beams, and the reference beams. For initial linear polarizations and propagation directions for the measurement beam and the progenitor beam, the plurality of reflective surfaces can be oriented to preserve a linear polarization for the measurement beam, the portions of the measurement beam, a progenitor beam for the reference beams, and the reference beams upon their successive reflections.

In general, in another aspect, the invention features an interferometry system including an interferometer, a control circuit, and an angle measurement system. During operation the interferometer directs a measurement beam along a measurement path contacting a measurement object, separates the measurement beam into m portions, e.g., where m is one of 2 and 3, and recombines at least a part of one of the portions with each of the remaining m−1 portions to form m−1 overlapping pairs of exit beams. The interferometer includes a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element. The beam steering element is positioned to direct the measurement beam to the measurement object and receive the m separated portions, the measurement beam and each of the m separated portions contacting the beam steering element. During operation the control circuit causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object, and the angle measurement system calculates the change in angular orientation of the measurement object based on at least one of interferometric signals derived from the m−1 overlapping pairs of exit beams and the reorientation of the beam steering element.

In some embodiments, the interferometer further includes a plurality of reflective surfaces oriented to direct the measurement beam and the portions of the measurement beam. For an initial linear polarization and propagation direction for the measurement beam, the plurality of reflective surfaces can be oriented to preserve a linear polarization for the measurement beam and the portions of the measurement beam upon their successive reflections.

In general, in another aspect, the invention features an interferometry system including an interferometer, a control circuit, and an angle measurement system. During operation the interferometer directs two measurement beams along corresponding measurement paths contacting a measurement object and combines the measurement beam to form an overlapping pair of exit beams. The interferometer includes a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element. The beam steering element is positioned to direct the two measurement beams to the measurement object, the two measurement beams contacting the beam steering element. During operation the control circuit causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object and the angle measurement system calculates the change in angular orientation of the measurement object based on at least one of an interferometric signal derived from the overlapping pair of exit beams and the reorientation of the beam steering element. In some embodiments, the two measurement beams to contact the measurement object at substantially the same location.

In some embodiments, the interferometer further includes a plurality of reflective surfaces oriented to direct the measurement beams. For an initial linear polarization and propagation direction for a progenitor beam for the measurement beams, the plurality of reflective surfaces can be oriented to preserve a linear polarization for the measurement beams upon their successive reflections.

In general, in another aspect, the invention features an interferometry system including an interferometer, a beam steering assembly, a control circuit, and an angle measurement system. During operation the interferometer receives an input beam, splits the input beam into a measurement beam and m reference beams, where m is an integer greater than 1, directs the measurement beam along a measurement path contacting a measurement object, and combines each of m portions of the measurement beam with a corresponding one of the m reference beams to form m overlapping pairs of exit beams. The beam steering assembly has a beam steering element and a positioning system to orient the beam steering element. The beam steering element is positioned to direct the input beam and the m overlapping pairs of exit beams, the input beam and the m overlapping pairs of exit beams contacting the beam steering element. During operation, the control circuit causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object and the angle measurement system calculates the change in angular orientation of the measurement object based on at least one of interferometric signals derived from the m overlapping pairs of exit beams and the reorientation of the beam steering element.

In some embodiments, the interferometer further includes a plurality of reflective surfaces oriented to direct the measurement beam and the reference beams. For an initial linear polarization and propagation direction for the input beam, the plurality of reflective surfaces can be oriented to preserve a linear polarization for the measurement beam and the reference beams upon their successive reflections.

In general, in another aspect, the invention features an interferometry system including an interferometer, a beam steering assembly, a control circuit, and an angle measurement system. During operation the interferometer receives an input beam, splits the input beam into two measurement beams, directs the measurement beams along respective measurement paths contacting the measurement object, and combines the measurement beams to form an overlapping pair of exit beams. The beam steering assembly has a beam steering element and a positioning system to orient the beam steering element. The beam steering element is positioned to direct the input beam and the overlapping pair of exit beams, the input beam and the overlapping pair of exit beams contacting the beam steering element. During operation, the control circuit causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object and the angle measurement system calculates the change in angular orientation of the measurement object based on at least one of an interferometric signal derived from the overlapping pair of exit beams and the reorientation of the beam steering element.

In some embodiments, the interferometer further includes a plurality of reflective surfaces oriented to direct the measurement beams. For an initial linear polarization and propagation direction for the input beam, the plurality of reflective surfaces can be oriented to preserve a linear polarization for the measurement beams upon their successive reflections.

In general, in another aspect, the invention features an interferometry system including an interferometer, a control circuit, and an angle measurement system. During operation, the interferometer directs a measurement beam along a measurement path contacting a measurement object, separates the measurement beam into first and second portions, directs the first and second portions along separate paths, and subsequently recombines the first and second portions with each other to form at least one overlapping pair of exit beams. The interferometer includes a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element being positioned to direct the measurement beam to the measurement object and subsequently receive the measurement beam from the measurement object. The measurement beam thereby twice contacts the beam steering element, after which the interferometer separates the measurement beam into the first and second portions. During operation, the control circuit causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object based on at least one interferometric signal derived from the at least one overlapping pair of exit beams. During operation, the angle measurement system calculates the change in angular orientation of the measurement object based on the reorientation of the beam steering element.

In some embodiments, the interferometer recombines the first and second portions into two overlapping pairs of exit beams, and the at least one interferometric signal is at least two interferometric signals derived from the two overlapping pairs of exit beams. The control circuit includes two detection channels which during operation measure the at least two interferometric signals, one of the detection channels including a quarter wave plate oriented to cause the two interferometric signals to be in quadrature with one another.

Also, in some embodiments, the interferometer separates the measurement beam into third and fourth portions after the measurement beam twice contacts the beam steering element, directs the third and fourth portions along separate paths, and recombines the third and fourth portions to form a second at least one pair of overlapping exit beams. During operation the control circuit causes the positioning system to reorient the beam steering element along two dimensions based on the at least one interferometric signal and a second at least one interferometric signal derived from the second at least pair of overlapping exit beams.

Furthermore, in some embodiments, the interferometer can further separate the measurement beam into an additional portion after the measurement beam twice contacts the beam steering element and combines the additional portion with a reference beam to form an additional pair of overlapping exit beams. The interferometry system further includes a distance measurement system, which during operation measures changes in distance to the measurement object based on an interferometric signal derived from the additional pair of overlapping exit beams.

Also, in some embodiments, the interferometer further includes a plurality of reflective surfaces oriented to direct the measurement beam and the portions of the measurement beam. For an initial linear polarization and propagation direction for the measurement beam, the plurality of reflective surfaces can be oriented to preserve a linear polarization for the measurement beam and the portions of the measurement beam upon their successive reflections.

Embodiments of any of the interferometry systems described above can include any of the following features.

The angle measurement system can calculate the change in angular orientation of the measurement object based on the reorientation of the beam steering element or it can calculate the change in angular orientation of the measurement object based on the interferometric signal(s) derived from the overlapping pair(s) of exit beams. The angle measurement system can calculate the change in angular orientation of the measurement object along two dimensions. The angle measurement system can further calculate changes in distance to the measurement object based on at least one of the interferometric signal(s) derived from the overlapping pair(s) of exit beams. The control circuit can cause the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object. The control circuit can generate a servo signal based on the interferometric signal(s) derived from the overlapping pair(s) of exit beams and can cause the positioning system to reorient the beam steering element (e.g., along one or two dimensions) in response to the change in angular orientation of the measurement object based on the servo signal.

Alternatively, the control circuit can include a detector having spatially resolved detector elements operative to measure the position and/or direction of at least a portion of the overlapping pair(s) of exit beams. The control signal generates a servo signal based on the measured position and/or direction and causes the positioning system to reorient the beam steering element (e.g., along one or two dimensions) in response to the change in angular orientation of the measurement object based on the servo signal. The detector can be operative to measure the difference in position and/or direction between the exit beams of at least one of the overlapping pair(s) of exit beams. Alternatively, the detector can be operative to measure the position and/or direction of the measurement beam component of at least one of the overlapping pair(s) of exit beams relative to a reference position and/or direction.

The invention also features a lithography system for fabricating integrated circuits including first and second components, which are movable relative to one another. One of interferometry systems described above is secured to the second component and the measurement object is a mirror rigidly secured to the first component. During operation the interferometry system measures the position of the first component relative to the second component. In some embodiments, the second component is a movable stage used to support a wafer and during operation the beam steering element causes the measurement beam to contact the mirror at substantially normal incidence over a range of angular orientations of the measurement object.

In another aspect, the invention also features a lithography system for use in fabricating integrated circuits on a wafer. The lithography system includes: a stage for supporting the wafer; an illumination system for imaging spatially patterned radiation onto the wafer; a positioning system for adjusting the position of the stage relative to the imaged radiation; and at least one of any of the interferometry systems described above. The interferometry system(s) measures the position of the wafer relative to the imaged radiation.

In another aspect, the invention features a lithography system for use in fabricating integrated circuits on a wafer. The lithography system includes a stage for supporting the wafer and an illumination system. The illumination system includes a radiation source, a mask, a positioning system, a lens assembly, and at least one of any of the interferometry systems described above. During operation the source directs radiation through the mask to produce spatially patterned radiation. The positioning system adjusts the position of the mask relative to the radiation from the source. The lens assembly images the spatially patterned radiation onto the wafer. The interferometry system(s) measures the position of the mask relative to the radiation from the source.

In another aspect, the invention features a lithography system for fabricating integrated circuits. The lithography system includes first and second components, the first and second components being movable relative to each other. The lithography system also includes at least one of any of the interferometry systems described above, wherein the first component includes the measurement object and the interferometry system(s) monitors the position of the first component relative to the second component.

In another aspect, the invention features a beam writing system for use in fabricating a lithography mask. The beam writing system includes: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and at least one of any of the inteferometry systems described above for measuring the position of the stage relative to the beam directing assembly.

In general, in another aspect, the invention features an interferometry method including: directing a measurement beam along a measurement path contacting a measurement object; combining at least a portion of the measurement beam with another beam to form an overlapping pair of exit beams; using an electronic control system to redirect the measurement beam in response to a change in the angular orientation of the measurement object based on a servo signal derived from at least a portion of the overlapping pair of exit beams; and calculating the change in angular orientation based on an interferometric signal derived from the overlapping pair of exit beams and the redirection of the measurement object. In some embodiments, using the electronic control system includes redirecting the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.

In another aspect, the invention features a lithography method for use in fabricating integrated circuits. The lithography method includes: imaging spatially patterned radiation onto a wafer; positioning the wafer relative to the imaged radiation; and measuring the position of the wafer relative to the imaged radiation using at least one of the interferometry methods described above.

In another aspect, the invention features a lithography method for use in the fabrication of integrated circuits. The lithography method includes: directing input radiation through a mask to produce spatially patterned radiation; positioning the mask relative to the input radiation; measuring the position of the mask relative to the input radiation using at least one of the interferometry methods described above; and imaging the spatially patterned radiation onto a wafer.

In another aspect, the invention features a lithography method for use in fabricating integrated chips. The lithography method includes: positioning a first component of a lithography system relative to a second component of a lithography system to expose a wafer to spatially patterned radiation; and measuring the position of the first component relative to the second component using any of the interferometry methods described above.

In another aspect, the invention features a beam writing method for use in fabricating a lithography mask. The method includes: directing a write beam to a substrate to pattern the susbtrate; positioning the substrate relative to the write beam; and measuring the position of the substrate relative to the write beam using any of the interferometry methods described above.

Embodiments of the interferometry systems and methods described above include many advantages.

The interferometry systems can measure changes in the angular orientation of a measurement object. Furthermore, some embodiments can measure changes in the angular orientation along two dimensions and/or can also measure changes in distance to the measurement object. In addition, many embodiments measure the changes in angular orientation with only a single beam contacting the measurement object or with multiple beams contacting the measurement object at a single location. Thus, the reflective surface of the measurement object can be relatively small. In particular, some of interferometry systems can measure changes in displacement, pitch, and yaw of a stage mirror with a footprint on the stage mirror of only a single beam spot. Moreover, when the measurement beam includes multiple wavelengths, the effects of dispersion along the single beam path to the measurement object can be measured and used to calculate values for displacement, pitch, and/or yaw that are corrected for air-turbulence.

Also, for each of the overlapping pairs of exit beams the interferometry system maintains the overlap of the respective exit beams substantially parallel to one another over a range of orientations of the measurement object, and can do so with only a single pass of the measurement beam to the measurement object. The single-pass embodiments reduce the bandwidth of electronics needed to process electrical interference signals having Doppler shifts, relative to those of a double-pass interferometer. Furthermore, the single-pass embodiments reduce the likelihood of depolarization, scattering, and undesired spurious reflections from transmissive optics within the interferometer, relative to those for a double-pass interferometer. Such effects can introduce errors, e.g., cyclic errors, in the measured phase of the electrical interference signal.

Moreover, the system can minimize the transverse displacement between the exit beams of each overlapping pair of exit beams or the transverse displacement of components of such exit beams within the interferometer, caused by changes in the angular orientation of the measurement object. As a result, the average amplitude of the electrical interference signal derived from optically mixed exit beams can be substantially independent of changes in the angular orientation and position of the measurement object. In addition, the system reduces changes of the paths of the beams through transmissive optics of the interferometer, e.g., polarizing beam splitters and quarter wave plates, caused by changes in the angular orientation or position of the measurement object. Such transmissive optics can have imperfections in their surface figures and local variations in refractive index. Thus, changes in the paths of the beams through such optics can change the optical path length measured by the interferometer even though the distance between the measurement object and the interferometer has not changed. Such negative effects can be compounded if a transmissive optic has dispersive properties, such as those produced by a wedge. Finally, some embodiments of the invention can be made in compact configurations and include optical configurations that minimize the introduction of ellipticity into the linear polarization of beams directed by the optical configuration.

Other features, aspects, and advantages will be clear from the following detailed description and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic drawing of a first embodiment of the interferometry system.

FIG. 2 is a schematic drawing of a second embodiment of the interferometry system.

FIG. 3 is a schematic drawing of a third embodiment of the interferometry system.

FIG. 4 is a schematic drawing of a fourth embodiment of the interferometry system.

FIGS. 5a-b are schematic drawings of a fifth embodiment of the interferometry system and

FIGS. 5c-g are schematic drawings of a variant of the fifth embodiment.

FIGS. 6a-b are schematic drawings of a sixth embodiment of the interferometry system and

FIGS. 6c-g are schematic drawings of a variant of the sixth embodiment.

FIGS. 7a-c are schematic drawings of a seventh embodiment of the interferometry system and

FIGS. 7d-f are schematic drawings of a variant of the seventh embodiment.

FIGS. 8a-c are schematic drawings of an eighth embodiment of the interferometry system.

FIGS. 9a-c relate to lithography and its application to manufacturing integrated circuits.

FIG. 9a is a schematic drawing of a lithography exposure system employing the interferometry system.

FIGS. 9b and 9 c are flow charts describing steps in manufacturing integrated circuits.

FIG. 10 is a schematic of a beam writing system employing the interferometry system.

FIG. 11a-e are schematic drawings of a ninth embodiment of the interferometry system.

DETAILED DESCRIPTION

The present invention relates to apparatus and methods by which an angular displacement of a measurement object or angular and linear displacements of the object may be quickly measured for subsequent use in a contemporaneous downstream application. An example of an application is in an interferometric angular displacement and linear displacement-measuring instrument to measure and monitor the orientation and position of a mask stage or a wafer stage in a lithographic scanner or stepper system.

A first set of embodiments of the invention feature an angular displacement interferometry system including an interferometer and at least one beam-steering assembly controlled by a control circuit. The angle displacement interferometer may comprise a single interferometer, an interferometer system comprising two or more linear displacement interferometers in an integrated “non-stacked” configuration. Certain of the angle displacement interferometers operate in a “null” or differential mode and certain other of the angle displacement interferometers operate in a displacement or non-differential mode.

A second set of embodiments of the invention features an angular displacement and linear displacement interferometry system including at least one angular displacement interferometer such as comprising the first set of embodiments, at least one linear displacement interferometer, and at least one beam-steering assembly controlled by a control circuit. In some embodiments from the first set and in some embodiments from the second set, the beam-steering assembly is a component of the interferometer or interferometers, directing at least one of the reference and measurement beams within the interferometer or interferometers. In other embodiments from the first set and in other embodiments from the second set, the beam-steering assembly is separate from the interferometer or interferometers, the beam-steering assembly directing an input beam to and an output beam from the interferometer or interferometers. The beam-steering assembly redirects one or more of the input, output, reference, and measurement beams to minimize undesired consequences of changes in the angular orientation or position of the measurement object.

Beam steering assemblies, control circuits, and their uses in displacement measuring interferometry are described in copending, commonly owned U.S. patent application having Ser. No. 09/157,131, filed Oct. 18, 1998, and entitled “Interferometer Having A Dynamic Beam Steering Assembly” by H. A. Hill and P. de Groot, the contents of which are incorporated herein by reference.

A schematic of a first embodiment of the invention is shown in FIG. 1. The first embodiment is from the first set of embodiments comprising a single interferometer operating in a null or differential mode with the beam-steering assembly redirecting both the reference and measurement beams of the interferometer. A polarizing beam-splitter assembly 40 with polarizing interface 40A and reflecting surface 40B in an interferometer 10 receives an input beam 14 from a laser source (not shown) and separates input beam 14 into a reference beam 15 and a measurement beam which is reflected by surface 40B as measurement beam 16. Reference beam 15 and measurement beam 16 have orthogonal linear polarizations. Polarizing beam-splitting interface 40A reflects beams having a polarization orthogonal to the plane of FIG. 1 and transmits beams having a polarization parallel to the plane of FIG. 1.

In the described embodiment, the orthogonally polarized reference and measurement beams are frequency-shifted with respect one another, e.g., by Zeeman splitting, acousto-optic modulation, or by use of birefringent elements internal to the laser, prior to entering interferometer 10 as components of input beam 14. The different frequencies enable the interferometry system to generate a heterodyne interference signal. Although the described embodiment is a heterodyne system, the instant invention is readily adapted for use in a homodyne system in which the reference and measurement beams have the same frequencies.

The source such as a laser can be any of a variety of frequency modulation apparatus and/or lasers. For example, the laser can be a gas laser, e.g., a HeNe laser, stabilized in any of a variety of conventional techniques known to those skilled in the art, see for example, T. Baer et al., “Frequency Stabilization of a 0.633 μm He—Ne-longitudinal Zeeman Laser,” Applied Optics, 19, 3173-3177 (1980); Burgwald et al., U.S. Pat. No. 3,889,207, issued Jun. 10, 1975; and Sandstrom et al., U.S. Pat. No. 3,662,279, issued May 9, 1972. Alternatively, the laser can be a diode laser frequency stabilized in one of a variety of conventional techniques known to those skilled in the art, see for example, T. Okoshi and K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-type Optical Communication Systems,” Electronic Letters, 16, 179-181 (1980) and S. Yamaqguchi and M. Suzuki, “Simultaneous Stabilization of the Frequency and Power of an AlGaAs Semiconductor Laser by Use of the Optogalvanic Effect of Krypton,” IEEE J. Quantum Electronics, QE-19, 1514-1519 (1983).

Two optical frequencies may be produced by one of the following techniques: (1) use of a Zeeman split laser, see for example, Bagley et al., U.S. Pat. No. 3,458,259, issued Jul. 29, 1969; G. Bouwhuis, “Interferometrie Mit Gaslasers,” Ned. T. Natuurk, 34, 225-232 (August 1968); Bagley et al., U.S. Pat. No. 3,656,853, issued Apr. 18, 1972; and H. Matsumoto, “Recent interferometric measurements using stabilized lasers,” Precision Engineering, 6(2), 87-94 (1984); (2) use of a pair of acousto-optical Bragg cells, see for example, Y. Ohtsuka and K. Itoh, “Two-frequency Laser Interferometer for Small Displacement Measurements in a Low Frequency Range,” Applied Optics, 18(2), 219-224 (1979); N. Massie et al., “Measuring Laser Flow Fields With a 64-Channel Heterodyne Interferometer,” Applied Optics, 22(14), 2141-2151 (1983); Y. Ohtsuka and M. Tsubokawa, “Dynamic Two-frequency Interferometry for Small Displacement Measurements,” Optics and Laser Technology, 16, 25-29 (1984); H. Matsumoto, ibid.; P. Dirksen, et al., U.S. Pat. No. 5,485,272, issued Jan. 16, 1996; N. A. Riza and M. M. K. Howlader, “Acousto-optic system for the generation and control of tunable low-frequency signals,” Opt. Eng., 35(4), 920-925 (1996); (3) use of a single acousto-optic Bragg cell, see for example, G. E. Sommargren, commonly owned U.S. Pat. No. 4,684,828, issued Aug. 4, 1987; G. E. Sommargren, commonly owned U.S. Pat. No. 4,687,958, issued Aug. 18, 1987; P. Dirksen, et al., ibid.; (4) use of two longitudinal modes of a randomly polarized HeNe laser, see for example, J. B. Ferguson and R. H. Morris, “Single Mode Collapse in 6328 Å HeNe Lasers,” Applied Optics, 17(18), 2924-2929 (1978); (5) use of birefringent elements or the like internal to the laser, see for example, V. Evtuhov and A. E. Siegman, “A “Twisted-Mode” Technique for Obtaining Axially Uniform Energy Density in a Laser Cavity,” Applied Optics, 4(1), 142-143 (1965); or the use of the systems described in U.S. patent application with Ser. No. 09/061,928 filed Apr. 17, 1998 entitled “Apparatus to Transform Two Non-Parallel Propagating Optical Beam Components into Two Orthogonally Polarized Beam Components” by H. A. Hill, the contents of which are incorporated herein by reference.

The specific device used for the source of beam 14 will determine the diameter and divergence of beam 14. For some sources, e.g., a diode laser, it will likely be necessary to use conventional beam shaping optics, e.g., a conventional microscope objective, to provide beam 14 with a suitable diameter and divergence for elements that follow. When the source is a HeNe laser, for example, beam-shaping optics may not be required.

Reflecting surface 40B of beam-splitting assembly 40 directs measurement beam 16 to a beam-steering assembly 12 which includes a beam-steering mirror 60 and a pair of piezoelectric transducers 62A and 623B. The transducers are coupled to beam-steering mirror 60 by flexures to orient beam-steering mirror 60 in response to a signal 78 from a servo controller 84. Beam-steering assembly 12 includes capacitance gauges, interferometers or the like to measure changes in orientation and/or position of beam-steering mirror 60. The capacitance gauges or interferometers may also be used to measure and/or monitor the properties of piezoelectric transducers 62A and 62B.

Beam-steering assembly 12 directs measurement beam 16 to contact a measurement object mirror 66 at substantially normal incidence. Measurement object mirror 66 then reflects the measurement beam back to retrace its path to beam-steering assembly 12 and polarizing beam-splitter assembly 40. The measurement beam double passes a quarter wave plate 70, which is positioned between beam-steering assembly 12 and polarizing beam-splitter assembly 40 and which rotates the linear polarization of the measurement beam by 90°.

Rhomb 41 comprising reflecting surfaces 41A and 41B directs reference beam 15 to the beam-steering assembly 12, which in turn directs the reference beam to contact measurement object mirror 66. Measurement object mirror 66 then reflects the reference beam back to retrace its path to beam-steering assembly 12, through rhomb 41, and to polarizing beam-splitter assembly 40. The reference beam also double passes a quarter wave plate 71 which rotates the linear polarization of the reference beam by 90°.

Polarizing beam-splitter assembly 40 then recombines the polarization-rotated reference and measurement beams to form overlapping output reference and measurement beams which together form an output beam 20. Output beam 20 passes through a polarizer 72 which mixes polarizations of the output reference and measurement beams to form a mixed output beam 22. Interferometer system 10 and measurement object mirror 66 introduce a relative phase shift φ₁ between the measurement and reference beam components of mixed output beam 22. A signal detection and processing system 82 measures the intensity of mixed output beam 22, e.g., preferably by photoelectric detection, to produce an electrical interference signal or electrical heterodyne signal s₁, extracts phase φ₁ of s₁, and determines from phase φ₁ an error related to relative orientations of measurement object mirror 66 and steering mirror 60.

Signal s₁ has the form

s ₁ =A ₁(t)cos[α₁(t)].  (1)

The phase α₁ may be extracted by either digital or analog signal processes, preferably digital processes, using time-based phase detection such as a digital Hilbert transform phase detector [see “Phase-locked loops: theory, design, and applications” 2nd ed. (McGraw-Hill, New York) 1993, by R. E. Best], a phase-locked loop [see R. E. Best, ibid.], a sliding window FFT [see Digital Techniques for Wideband Receivers, (Artech House, Boston) 1995, by J. Tsui], or the like and a reference phase. In applications where an acousto-optical modulator is used to generate the frequency splitting of the input beam, the reference phase may be obtained from an electronic driver of an acousto-optical modulator. Alternatively, the reference phase may be generated by an optical pick-off means and detector (not shown in figure) by splitting off a portion of beam 14 with a non-polarizing beam splitter, mixing the split-off portion of the beam 14, and detecting the mixed portion to produce an alternative heterodyne reference signal and associated reference phase.

A determination of phase α₁ is described further in terms of a digital Hilbert transform phase detector. Signal s₁ is the real part, ŝ_(1,R), of a complex number ŝ₁ where s₁ comprises a causal, stable, i.e., absolutely summable, real sequence. Thus, the Fourier transform S_(1,R)(jω) of s₁ completely defines S₁(jω) [see Chapter 10 “Discrete Hilbert Transforms” in Discrete-Time Signal Processing, (Prentice Hall, 1989) by A. V. Oppenheim and R. W. Schafer] where

S ₁(jω)=S_(1,R)(jω)+jS _(1,I)(jω),  (2)

S_(1,I),(jω) is the imaginary component of S₁(jω), ω is an angular frequency, and j is the imaginary number {square root over ((−1+L ))}.

The imaginary component ŝ_(1,I) of ŝ₁ is obtained from the inverse Fourier transform of S_(1,I)(jω) with

s _(1,I) =A ₁(t)sin[α₁(t)].  (3)

The phase α₁(t) can be obtained from ŝ_(1,R) and ŝ_(1,I) according to the formula $\begin{matrix} {{\alpha_{1}(t)} = {{\arctan \left( \frac{s_{1,I}}{s_{1,R}} \right)}.}} & (4) \end{matrix}$

The time-dependent argument α₁(t) is expressed in terms of other quantities according to the formula

 α_(i)(t)=2πf ₁ t+φ _(i)+ζ_(i)+Λ_(i)  (5)

where i is an index denoting reference to a particular embodiment, and where Λ_(i) comprises the nonlinear errors including in particular cyclic error terms and phase offset ζ_(i) comprises all contributions to phase α_(i) that are not related or associated with the optical path of the measurement and reference paths and not related to the nonlinear errors. Phase offset ζ₁ is generally considered a constant in the first embodiment of the invention and is measured and/or monitored as required by an end use application using known techniques.

Phase ζ₁ is given by the formula

φ₁ =k[∫ _(M) nds−∫ _(R) nds]  (6)

where the integrals are line integrals with respect to the infinitesimal optical path length nds along the measurement and reference paths indicated by M and R, respectively, and n is the refractive index of the infinitesimal physical path length ds at the wavelength λ of input beam 14. Phase φ₁ is also related to the deviation from normal incidence δθ₁ of the reference and measurement beams on stage mirror 66 in the plane of FIG. 1 according to the expression $\begin{matrix} {\phi_{1} = {2{ka}\quad \frac{\tan \quad \delta \quad \theta_{1}}{1 + {\tan \quad \delta \quad \theta_{1}}}}} & (7) \end{matrix}$

where k is the wavenumber 2π/λ and a is the separation of reference and measurement beams 15 and 16 (see FIG. 1).

Signal detector and processor system 82 determines error δθ₁ from the measured value of φ₁ using Eq. (7) and sends an error signal 76 based on error δθ₁, indicative of any error in the orientation of stage mirror 66 relative to beam-steering mirror 60, to servo controller 84. Servo controller 84 sends signal 78 to beam-steering assembly 12 in response to error signal 76. Beam-steering assembly 12 changes, in response to signal 78, the orientation of beam-steering mirror 60 preferably about a point on the reflecting surface of beam-steering mirror 60 midway between the locations where reference and measurement beams are reflected thereon. Changes in orientation of beam-steering mirror 60 about the point on beam-steering mirror 60 rather than some other point generally produces substantially reduced lateral shear effects experienced by the reference and measurement beams at and post beam-steering mirror 60.

A change in the angular orientation of measurement object mirror 66 without a compensating change in the orientation of beam-steering mirror 60 changes the directions of propagation of the reference and measurement beams and the direction of propagation of subsequent output beam 20 although the reference and measurement beam components of beam 20 remain parallel. The changes in direction of the reference and measurement beams causes the optical path lengths of the reference and measurement beams to change, one relative to the other, and causes detector and processor system 82 to generate error signal 76. Servo-controller 84 responds to the error signal by directing beam-steering assembly 12 to reorient beam-steering mirror 60 so as to minimize the error signal, e.g., by directing the reference and measurement beams to measurement object mirror 66 at normal incidence.

The classification of the first embodiment as comprising an interferometer operating in a null or differential mode is in recognition that only an error in the orientation of the measurement object mirror relative to the beam-steering mirror is measured by the processor system 82.

The angular change in the orientation of beam-steering mirror 60 is equal to one half of the corresponding change in the orientation of measurement object mirror 66 when the servo control signal is zero. In addition to the exit reference and measurement beam components of beam 20 remaining substantially parallel to one another, the position of output beam 20 remains substantially constant over a range of angular orientations of measurement object mirror 66. Furthermore, because the angles of incidence of reference and measurement beams on beam-steering mirror 60 are substantially equal, a translation of beam-steering mirror 60 in a direction normal to the reflecting surface of beam-steering mirror 60 does not introduce a change in the relative optical path length between the reference and measurement beams to first and higher orders in the translation.

The relative orientation of measurement object mirror 66 in the plane of FIG. 1 can be measured and monitored by measuring and monitoring the relative orientation of beam-steering mirror 60. This option is available as a direct consequence of a system property wherein an angular change in the orientation of beam-steering mirror 60 is equal to one half of the corresponding change in the orientation of measurement object mirror 66. Thus, an angle measuring system 83 calculates the change in angular orientation of measurement object mirror 66 based on the change in angular orientation of beam-steering mirror 60. In the presently described embodiment, angle measuring system 83 directly measures the change in orientation of beam steering mirror 60 by using, for example, calibrated capacitance gauges incorporated into beam steering assembly 12. Alternatively, in other embodiments, angle measurement system 83 includes calibration data for beam-steering assembly 12 that correlates the servo signal 76 to transducers 62A and 62B with the change in angular orientation of the beam steering mirror 60, which is directly related to the change in angular orientation of measurement object mirror 66 as described above. In such embodiments the angle measurement system calculates the angular orientation of the measurement object based on the servo signal.

Angle measuring system 83 can be calibrated interferometrically by operating the interferometer system of the first embodiment in an offset mode. In the offset mode of operation, an offset in orientation of measurement object mirror 66 relative to beam-steering mirror 60 is introduced and Eq. (7) used to convert, with a measurement of a, the corresponding measured change in phase φ₁ to a change in angular orientation of beam steering mirror 60. The offset in orientation can be introduced in one of several different ways. One example is the introduction of an offset, in either digital or analog format, to error signal 76 by additional electronic means (not shown in FIG. 1) with the servo control of beam steering mirror 60 operational.

Cyclic error contributions to Λ₁ can be reduced and/or measured and compensated in part or whole, as required by an end use application, with the incorporation into the first embodiment methods and apparatus such as described in G. Wilkening and W. Hou, U.S. Pat. No. 5,331,400 entitled “Heterodyne Interferometer Arrangement” issued Jul. 19, 1994; in copending, commonly owned U.S. patent application with Ser. No. 09/168,200 by S. R. Paterson, V. G. Bagdami, and C. A. Zanoni entitled “Interferometry System Having Reduced Cyclic Errors” filed Oct. 6, 1998; and in copending, commonly owned U.S. patent application with Ser. No. 09/268,619 now U.S. Pat. No. 6,137,574 filed Oct. 4, 2000 by H. A. Hill entitled “Systems and Methods For Characterizing Cyclic Errors In Distance Measuring and Dispersion Interferometry” filed Mar. 16, 1999. The contents of the two copending applications are incorporated herein by reference.

Gas in a reference path and/or measurement path can introduce an error in the angular orientation of measurement object mirror 66 inferred from the angular orientation of beam-steering mirror 60 due to the effects of density gradients in the gas. Density gradients in the gas alter the directions of propagation of reference and/or measurement beams propagating through the gas. For further description of the error in angular orientation, see the description of corresponding effects of gas given for the second embodiment of the present invention.

A variant of the first embodiment is described in which an angular displacement of an object in two orthogonal planes is measured and monitored. The variant of the first embodiment comprises the same input beam 14 and interferometer system 10 plus an additional set of optical elements, detector and signal processor system, and beam-steering assembly transducers. The additional set of optical elements comprise elements the same as elements 40, 41, 70, and 71 whose plane is rotated to be orthogonal to the plane of FIG. 1 about a line approximately parallel to the vertical direction in FIG. 1. A portion of input beam 14 is split off by a non-polarizing beam splitter (not shown) and used as an input beam to the additional set of optical elements. The additional reference and measurement beams generated by the additional set of optical elements are incident on beam-steering assembly 12 and measurement object mirror 66 and generate an additional output beam. The description of the propagation of the additional reference and measurement beams and the generation of the additional output beam is the same as corresponding portions of the description given for the reference, measurement, and output beams of the first embodiment.

The polarization components of the additional output beam are mixed by a polarizer (not shown), the same as polarizer 72, and the additional mixed beam is detected by the additional detector and processor system (not shown) functionally the same as detector and processor system 82. The additional detector and processor system generates an additional error signal that is sent to an additional servo controller (not shown) functionally the same as servo controller 84. The additional servo controller generates an additional signal that is transmitted to beam-steering assembly 12 for control of angular orientations of beam-steering mirror 60 by additional transducers (not shown) in a plane orthogonal to the plane of FIG. 1 and orthogonal to the reflecting surface of beam-steering mirror 60. The description of the additional transducers is the same as the corresponding portions of the description given for transducers 62A and 62B.

The remaining description of the variant of the first embodiment is the same as corresponding portions of the description given for the first embodiment.

A schematic of a second embodiment of the present invention is shown schematically FIG. 2. The second embodiment is from the first set of embodiments comprising two linear displacement interferometers in a non-stacked configuration and operating in non-null or displacement modes. In addition, a beam-steering assembly redirects the measurement beams of the two linear displacement interferometers. A polarizing beam splitter 140 in interferometer 110 receives an input beam 114 from a laser source (not shown) and separates input beam 114 into reference beam 116 and measurement beam 118. The description of the source of input beam 114, reference beam 116, and measurement beam 118 is the same as corresponding portions of descriptions given for the source of input beam 14, reference beam 16, and measurement beam 18, respectively, of the first embodiment.

Measurement beam 118 is incident on the beam-steering assembly 112 and reflected by beam-steering mirror 160 as measurement beam 120. The description of beam-steering assembly 112 comprising beam-steering mirror 160 and transducers 162A and 162B is the same as corresponding portions of the description given for beam-steering assembly 12 comprising beam-steering mirror 60 and transducers 62A and 62B of the first embodiment.

Measurement beam 120 is incident on beam-splitter assembly 142 and transmitted by polarizing interface 142A, transmitted by quarter-wave phase retardation plate 143, and incident on measurement object mirror 166 at substantially normal incidence. Measurement object mirror 166 then reflects the measurement beam back to retrace its path to beam-splitter assembly 142 where it is reflected by polarizing interface 140A as measurement beam 122. The measurement beam double passes quarter-wave phase retardation plate 143 which is positioned between measurement object mirror 166 and beam-splitter assembly 142 and which rotates the linear polarization of the measurement beam by 90°.

Measurement beam 122 is incident on beam-splitter assembly 144, reflected by surface 144A, and a portion thereof transmitted by non-polarizing interface 144B as a first measurement beam 124. A second portion of measurement beam 122 reflected by surface 144A is reflected by non-polarizing interface 144B as a second measurement beam 125. First and second measurement beams 124 and 125 are linearly polarized perpendicular to the plane of FIG. 2. First measurement beam 124 is reflected by beam-steering mirror 160 and by mirror 146 as a first measurement beam 126. Second measurement beam 125 is first reflected by mirror 148, reflected by beam-steering mirror 160, and then reflected by mirror 150 as a second measurement beam 127. As shown in FIG. 2, the spatial separation of the first and second measurement beams following reflection by beam-steering mirror 160 is a.

Reference beam 116 is incident on half-wave phase retardation plate 152 and transmitted as a reference beam with its plane of polarization rotated by 90°. The polarization rotated reference beam is incident on beam-splitter assembly 154, a first portion thereof reflected by non-polarizing interface 154B, and a portion of the first portion reflected by non-polarizing interface 154B then transmitted by non-polarizing interface 154A as a reference beam component of a first output beam 128. A second portion of the first portion of the polarization rotated reference beam reflected by non-polarizing interface 154B is reflected by non-polarizing interface 154A and then transmitted by quarter-wave phase retardation plate 156A as a reference beam component of a second output beam 130. A second portion of polarization rotated reference beam is transmitted by non-polarizing interface 154B, subsequently transmitted by polarizing interface 154C, and then transmitted by quarter-wave phase retardation plate 156A as a reference beam component of a third output beam 132.

First measurement beam 126 is incident on beam-splitter assembly 154 and a first portion thereof is reflected by non-polarizing interface 154A as a measurement beam component of the first output beam 128. A second portion of the first measurement beam 126 is transmitted by non-polarizing interface 154A and then transmitted by quarter-wave phase retardation plate 156A as a measurement beam component of the second output beam 130. Second measurement beam 127 is incident on beam-splitter assembly 154, reflected by surface 154D, reflected by polarizing interface 154C, and then transmitted by quarter-wave phase retardation plate 156B as a measurement beam component of the third output beam 132. The first and second output beams are mixed optical beams with respect to respective reference and measurement beam components by way of the quarter-wave phase retardation plates 156A and 156B.

First output beam 128 is incident on a detector system 182 which measures the difference in directions of propagation of the reference and measurement components of the first output beam 128. The difference in directions of propagation can be detected using well known techniques comprising combinations of imaging optics, multiple detectors, multi-element detectors, phase-shifting arrays to alter properties of images formed by the imaging optics, and interferometric imaging and signal processing techniques. Detector system 182 sends an error signal 176 indicative of any such difference to servo controller 184 which in turn sends signal 178 to beam-steering assembly 112 in response to error signal 176. Beam-steering assembly 112 changes, in response to signal 178, the orientation of beam-steering mirror 160 preferably about a point on the reflecting surface of beam-steering mirror 160 midway between the locations where first and second measurement beams contact beam-steering mirror 160. Changes in orientation about the point rather than some other point generally produces substantially reduced lateral shear effects experienced by the first and second measurement beams on beam-steering mirror 160.

Alternatively when the direction of the input beam 114 is constant, detector system 182 can measure a change in direction of propagation of the measurement beam component of first output beam 128 with respect to a reference direction in detector system 182 and generate error signal 178 indicative of that change in direction.

A change in the angular orientation of measurement object mirror 166 changes the direction of the first measurement beam and the direction of subsequent measurement beam component of first output beam 128. This causes detector system 182 to generate error signal 176. Servo-controller 184 responds to error signal 176 by directing beam-steering assembly 112 to reorient beam-steering mirror 160 so as to minimize error signal 176, e.g., by directing the measurement beam to measurement object mirror 166 at normal incidence.

As a result of the servo control operation to minimize error signal 176, the respective reference and measurement beam components of output beams 128, 130, and 132 remain substantially parallel, respectively, and the location of the paths of first, second, and third output beams 128, 130, and 132 remain substantially constant over a range of angular orientations of stage-mirror 166. Furthermore, since the angle of incidence of the first and second measurement beams on beam-steering mirror 160 are substantially equal, there is no first order effect of a translation of beam-steering mirror 160, particularly in a direction normal to the reflecting surface of beam-steering mirror 160, on the relative optical path length between the first and second measurement beams. These properties will be referenced hereinafter properties of a second system type.

Interferometer system 110 and measurement object mirror 166 introduce phase shifts φ₂ and φ₃ between the measurement beam and reference beam components of second and third output beams 130 and 132, respectively. Detector and signal processor system 180 measures the intensity of mixed beams 130 and 132, e.g., by photoelectric detection, to produce electrical interference signals or electrical heterodyne signals s₂ and s₃, respectively, extracts the phases φ₂ and φ₃ of the electrical heterodyne signals, s₂ and s₃, respectively, and determines from the phase difference φ³−φ₂ the angle θ₂ of measurement object mirror 166. Angle θ₂ is a relative orientation of a normal to the reflecting surface of measurement object mirror 166 in the plane of FIG. 2 and is computed using the formula $\begin{matrix} {{\theta_{2} = {{2{\arctan \quad\left\lbrack \frac{\eta_{2}}{1 + \eta_{2}} \right\rbrack}} - {\int{\left( \frac{\partial n_{M}}{\partial r} \right)\quad {s}}}}}{where}} & (8) \\ {{\eta_{2} = \left\lbrack \frac{\left( {\phi_{3} - \phi_{2}} \right)}{2n_{M}{ka}} \right\rbrack},} & (9) \end{matrix}$

the integration is along the optical path of the measurement beam components comprising a gas, and (∂n_(M)/∂s) partial derivative of the refractive index of the optical path of the measurement beam comprising the gas at a respective point along the measurement path with respect to a vector orthogonal to the optical path of the measurement beam and parallel to the plane of FIG. 2. The effects of gradients in the refractive index on the direction of propagation of a beam are described for example in an article entitled “Compensation for the Lateral Color Aberration Produced by the Atmosphere” by H. A. Hill and C. A. Zanoni, JOSA 56, 1655-1659 (1966). In the second embodiment, detector and signal processor system 180 form an angle detection system that directly calculates the relative angular orientation of measurement object mirror 166. Similar angle detection systems are also formed in subsequent embodiments unless otherwise specified.

The classification of the second embodiment as two linear displacement interferometers operating in an angular displacement mode, a non-null mode, is a result of the procedure wherein the difference in phase φ₃−φ₂ is not servoed to a zero value and is a direct measure of the relative orientation of the measurement object mirror as a function of time.

Turbulent effects of the gas are not present in the phase difference φ₃−φ₂ and therefore not present in η₂ since the measurement beams have substantially identical paths in the gas. Environmental and turbulent effects of the gas in the measurement path effect the measurement of the orientation of measurement object mirror 166 substantially only through environmental and turbulent effects on the gradient of the refractive index of the gas along the measurement path [see Eq. (8)].

Cyclic error contributions to Λ₃−Λ₂ can be reduced and/or measured and compensated in part or whole the same as described for the first embodiment. The description of the phase-offset difference ζ₃−ζ₂ is the same with respect to general properties and to measurement and monitoring as corresponding portions of the description given for phase offset in the first embodiment.

The phase difference φ₃−φ₂ may alternatively be obtained from the phase of a superheterodyne signal generated by mixing of electrical heterodyne signals s₂ and s₃. The Doppler shift contributions to φ₂ and φ₃, arising from motion of measurement object mirror 166, are substantially the same. Thus, Doppler shift effects are compensated in a superheterodyne phase φ₃−φ₂. A significant consequence is that the superheterodyne φ₃−φ₂ comprises substantially lower frequency components than do both φ₂ and φ₃. Thus, the acquisition of a measurement of phase difference φ₃−φ₂ to a given accuracy is generally a less demanding task when measuring phase φ₃−φ₂ directly as a superheterodyne phase in comparison to first making measurements of phases φ₂ and φ₃ individually and than computing the phase difference φ₃−φ₂.

The description of the advantage of the second embodiment vis-à-vis Doppler shift compensation is the same as corresponding portions of description given for the advantages of Doppler shift compensation in superheterodyne methods and apparatus in copending, commonly owned U.S. patent application with Ser. No. 09/252,206 filed Feb. 18, 1999 entitled “Interferometer And Method For Measuring The Refractive Index And Optical Path Length Effects of Air” by P. de Groot, H. A. Hill, and F. C. Demarest and U.S. patent application with Ser. No. 09/262,440 filed Feb. 18, 1999, now U.S. Pat. No. 6,219,144 filed Apr. 17, 2001, entitled “Apparatus And Method For Measuring The Refractive Index And Optical Path Length Effects Of Air Using Multiple-Pass Interferometry” by H. A. Hill, P. de Groot, and F. C. Demarest. The contents of both copending applications are incorporated herein by reference.

Note that θ₁ of the first embodiment and θ₂ of the second embodiment exhibit the same sensitivity to gradients in the refractive index of gas in respective measuring paths.

A variant of the second embodiment is described in which the angular displacement of an object in two orthogonal planes is measured and monitored. The description of the variant of the second embodiment in relation to the second embodiment is substantially the same as the description of the variant of the fifth embodiment in relation to the fifth embodiment of the present invention, which will be described further below.

FIG. 3 shows a schematic of a third embodiment of the present invention. The third embodiment is from the first set of embodiments comprising a single interferometer operating in a non-null or angular displacement mode. In addition, a beam-steering assembly redirects both the reference and measurement beams of the angular displacement interferometer. Certain of the elements and assemblies of the third embodiment perform like functions as like numbered elements and assemblies of the first embodiment shown in FIG. 1. The description of the certain of the elements and assemblies are the same as the description given for corresponding elements and assemblies of the first embodiment. Beam-splitting assembly 242 and quarter-wave phase retardation plate 243 are arranged so that the reference and measurement beams in a region between quarter-wave phase retardation plate 243 and measurement object mirror 66 are coextensive beams and thus propagate as coextensive beams in a gas in the region.

As shown in FIG. 3, beam-splitter assembly 40 directs reference beam 15 to rhomb 41. Rhomb 41 directs the reference beam to beam-steering assembly 12 that directs the reference beam to beam-splitter assembly 242. The reference beam is reflected by reflecting surface 242D, reflected by polarizing interface 242C, and directed to contact measurement object mirror 66 at substantially normal incidence. Measurement object mirror 66 then reflects the reference beam back to retrace its path to beam-splitter assembly 242. The reference beam double passes quarter-wave phase retardation plate 243 which rotates the linear polarization of the reference beam by 90°.

The polarization rotated reference beam is then transmitted by polarizing interface 242C, reflected by reflecting surfaces 242B and 242A, and directed to beam-steering mirror 60. The polarization rotated reference beam is reflected by beam-steering mirror 60 and directed to beam-splitter assembly 40. The polarization rotated reference beam is reflected by reflecting surface 40B and then reflected by polarizing interface 40A as a reference beam component of output beam 226.

As also shown in FIG. 3, beam-splitter assembly 40 directs measurement beam 16 to beam-steering assembly 12 which in turn directs the measurement beam to beam-splitter assembly 242. The measurement beam is reflected by reflecting surfaces 242A and 242B, transmitted by polarizing interface 242C, and directed to contact measurement object mirror 66 at substantially normal incidence. Measurement object mirror 66 then reflects the measurement beam back to retrace its path to beam-splitter assembly 242. The measurement beam double passes quarter-wave phase retardation plate 243 which rotates the linear polarization of the measurement beam by 90°.

The polarization rotated measurement beam is then reflected by polarizing interface 242C, reflected by reflecting surface 242D, and directed to beam-steering mirror 60. The polarization rotated measurement beam is reflected by beam-steering mirror 60 and directed to rhomb 41. The polarization rotated measurement beam is reflected by reflecting surfaces 41B and 41A and then transmitted by polarizing interface 40A as a measurement beam component of output beam 226.

Output beam 226 is incident on beam-splitter assembly 254 and a first portion thereof reflected by non-polarizing interface 254A as a first output beam 228. A second portion of the measurement beam 226 is transmitted by non-polarizing interface 254A and then transmitted by quarter-wave phase retardation plate 252 as second output beam 230. Second output beam 230 is a mixed optical beam with respect to respective reference and measurement beam components by way of the quarter-wave phase retardation plate 252.

The first output beam 228 is incident on a detector system 282 that generates error signal 276. The description of detector system 282 and error signal 276 is the same as corresponding portions of the description given for detector system 182 and error signal 176 of the second embodiment. Servo controller 84 receives error signal 276 and generates signal 278.

Interferometer system 210 and measurement object mirror 66 introduce a phase shift φ₄ between the measurement and reference components of mixed output beam 230 and detector and signal processor system 280 measures the intensity of mixed output beam 230, e.g., preferably by photoelectric detection, to produce electrical interference signal or electrical heterodyne signal s₄. Detector and signal processor system 280 extracts the phase of the electrical heterodyne signal s₄, determines phase φ₄ from the extracted phase, and determines the angle θ⁴ of stage mirror 66 from φ₄. The angle θ⁴ is a relative orientation of a normal to the reflecting surface of stage mirror 66 in the plane of FIG. 3 and computed using the formula $\begin{matrix} {{\theta_{4} = {{4{\arctan \quad\left\lbrack \frac{\eta_{4}}{1 + \eta_{4}} \right\rbrack}} - {\int{\left( \frac{\partial n}{\partial r} \right)\quad {s}}}}}{where}} & (10) \\ {{\eta_{4} = \left\lbrack \frac{\phi_{4}}{2n_{M}{ka}} \right\rbrack},} & (11) \end{matrix}$

the integration is along the optical path of the reference and measurement beams comprising a gas, and (∂n/∂s) is the partial derivative of the refractive index of the gas with respect to a vector orthogonal to the optical path of the reference and measurement beams and parallel to the plane of FIG. 3. As shown in FIG. 3, parameter a is the separation of measurement beam 16 and the reference beam generated by the redirection of reference beam 15 by rhomb 41.

Cyclic error contributions to Λ₄ can be reduced and/or measured and compensated in part or whole the same as described for the first embodiment. The description of the properties of the phase-offset difference ζ₄ and the measurement and monitoring thereof is the same as corresponding portions of the description given for phase offset of the first embodiment.

The description of the Eqs. (10) and (11), the relationship between the orientations of the beam-steering mirror and the measurement object mirror, and measured phases of the third embodiment are the same as corresponding portions of description given for the second embodiment, in particular the description given with respect to the superheterodyne mode of operation. The remaining description of the third embodiment is same as corresponding portions of descriptions given for the first and second embodiments.

A variant of the third embodiment is described in which the angular orientation of an object in two orthogonal planes is measured and monitored. The description of the variant of the third embodiment in terms of the third embodiment is substantially the same as the corresponding portion of the description given for the variant of the fifth embodiment in terms of the fifth embodiment, which will be described below.

A fourth embodiment of the present invention is described comprising an interferometer system and a dynamic-beam steering assembly for a measurement of the orientation of an object, e.g., a stage mirror. The fourth embodiment is from the first set of embodiments comprising a single angular displacement interferometer and operating in non-null or displacement mode. In addition, a beam-steering assembly redirects the reference and measurement beams of the angular displacement interferometer.

The fourth embodiment is shown schematically in FIGS. 4a and 4 b. The fourth embodiment comprises an interferometer with a beam-steering assembly redirecting both reference and measurement beams by a beam-redirecting element an even number of times in a manner to not be sensitive in first order to a linear displacement of the beam-redirecting element. The redirection of both reference and measurement beams of an interferometer by a beam-redirecting element an even number of times is feature of a system type the same as employed in the first embodiment of the present invention. The system type further comprises the reflection of both the reference beam and the measurement beam by the measurement object mirror where, at the measurement object mirror, the reference and measurement beams are substantially parallel and spatially separated.

A number of the elements of the fourth embodiment perform like functions as elements of the sixth embodiment described in copending, commonly owned U.S. patent application having Ser. No. 09/157,131 filed Oct. 18, 1998 and entitled “Interferometer Having A Dynamic Beam Steering Assembly” by H. A. Hill and P. de Groot. As described above, the contents of the copending application are incorporated herein by reference.

The element numbers of elements in FIGS. 4a and 4 b performing like functions in the fourth embodiment of the present invention are 300 less than the element numbers of the corresponding elements of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

The description of input beam 310 in FIG. 4a is the same as the description of input beam 14 of the first embodiment of the present invention. Beams 313, 315, 321, 329, 331, 333, 335, and 336 comprise reference and measurement beam components with corresponding reference and measurement beam components being orthogonally polarized. The description of measurement beam components of beams 313, 315, 321, 329, 331, 333, 335, and 336 is the same as corresponding portions of the description given for beams 613, 615, 621, 629, 631, 633, 635, and 636 of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131. Except for being in a different state of polarization, the description of reference beam components of beams 313, 315, 321, 329, 331, 333, 335, and 336 is otherwise the same as corresponding portions of the description for measurement beam components of 313, 315, 321, 329, 331, 333, 335, and 336.

The description of measurement beams 323 and 327 are the same as corresponding portions of the description given for measurement beams 623 and 627 of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

As shown in FIG. 4a, the reference beam component of beam 321 is reflected by polarizing beam splitter 358 as reference beam 324. Mirror 357 directs reference beam 324 to contact stage mirror 362. Stage mirror 362 then reflects the reference beam back to retrace its path to polarizing beam splitter 358 as reference beam 328. The reference beam also double passes a quarter-wave phase retardation plate 361 which rotates the linear polarization of the reference beam by 90°. The polarization-rotated reference beam is transmitted by polarizing beam splitter 358 as the reference beam component of beam 329.

Beam 336 comprises othogonally polarized reference and measurement beam components. A portion of beam 336 is reflected by non-polarizing beam splitter 374 as first output beam 338. The description beam 338, detector 376, and signal 344 is the same as corresponding portions of the description given of beam 638, detector 676, and signal 644 of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131. A second portion of 336 is transmitted by non-polarizing beam splitter 374 as a second output beam 340. Second output beam 340 is transmitted by polarizer 378 as a mixed output beam 342.

Interferometer system 300 and measurement object mirror 362 introduces a phase shift φ₅ between the measurement and reference beam components of mixed output beam 342. A detector 380 measures the intensity of mixed output beam 342, e.g., preferably by photoelectric detection, to produce electrical interference signal or electrical heterodyne signal S₅. Heterodyne signal S₅ is transmitted to electronic processor and computer 382 in either digital or analog format, preferably in digital format. Electronic processor and computer 382 extracts the phase of heterodyne signal s₅, determines phase φ₅ from the phase, and determines an orientation angle θ₅ of measurement object mirror 362 from phase φ₅. Angle θ₅ is an orientation of a normal to the reflecting surface of measurement object mirror 362 relative to a selected reference line, the normal and the reference line lying in the plane of FIG. 4a in the plane of FIG. 4a and is computed using the formula $\begin{matrix} {{\theta_{5} = {4{\arctan \quad\left\lbrack \frac{\eta_{5}}{1 + \eta_{5}} \right\rbrack}}}{where}} & (12) \\ {{\eta_{5} = \left\lbrack \frac{\phi_{5}}{2n_{M}{ka}} \right\rbrack},} & (13) \end{matrix}$

 φ₅ =k[∫ _(M) nds−∫ _(R) nds],  (14)

the integrations in Eq. (14) are along the respective measurement and reference optical paths portions of which include the gas, and parameter a is the separation of reference and measurement beams as shown in FIG. 4a.

The remaining description of the fourth embodiment is the same as corresponding portions of descriptions given for the first embodiment of the present invention and the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

A variant of the fourth embodiment of the present invention is described comprising two interferometers and a dynamic beam-steering assembly for a measurement of the orientation of an object, e.g., a stage mirror, in two orthogonal planes. The description of the variant of the fourth embodiment in terms of the fourth embodiment is substantially the same as the subsequently presented description of the variant of the fifth embodiment in terms of the fifth embodiment of the present invention, which will be described below.

A fifth embodiment of the present invention is described comprising an interferometer and a dynamic-beam steering assembly for a measurement of an orientation of an object, e.g., a stage mirror. The fifth embodiment is from the first set of embodiments comprising a single interferometer operating in a non-null or angular displacement mode. In addition, a beam-steering assembly redirects both the reference and measurement beams of the angular displacement interferometer. The fifth embodiment is shown schematically in FIGS. 5a and 5 b.

The fifth embodiment is of the second system type, the same as that employed in the second embodiment of the present invention, and comprises an interferometer with a dynamic beam-steering assembly redirecting both the reference and measurement beams of the interferometer by a beam-redirecting element an even number of times in a manner to not be sensitive in first order to a displacement of the beam-redirecting element. The second system type further comprises the reflection of a reference beam and measurement beam by the stage mirror where, at the measurement object mirror, the reference and measurement beams are coextensive having orthogonal states of polarization.

A number of the elements of the fifth embodiment perform like functions as elements of the sixth embodiment described in U.S. patent application having Ser. No. 09/157,131. The element numbers of elements in FIGS. 5a and 5 b performing like functions in the fifth embodiment of the present invention are 200 less than the element numbers of the corresponding elements of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

The description of input beam 410 in FIG. 5a is the same as the description given of input beam 14 of the first embodiment of the present invention. Beams 413, 415, 421, 423, 427, 429, 431, 435, and 436 comprise reference and measurement beam components with corresponding reference and measurement beam components having orthogonal states of polarization. The description of the measurement beam components of beams 413, 415, 421, 423, 427, 429, 431, 435, and 436 are the same as corresponding portions of the description given for beams 613, 615, 621, 623, 627, 629, 631, 635, and 636 of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131. Except for being in a different state of polarization, the description of reference beam components of beams 413, 415, 421, 423, 427, 429, 431, 435, and 436 is otherwise the same as corresponding portions of the description for measurement beam components of 413, 415, 421, 423, 427, 429, 431, 435, and 436.

In FIG. 5a, measurement beam component of beam 431 is transmitted by polarizing beam splitter 459A and reflected by beam-steering mirror 452 as measurement beam 433. Measurement beam 433 is reflected by mirror 466A and transmitted by polarizing beam splitter 466B as the measurement beam component of beam 435. Reference beam component of beam 431 is reflected by polarizing beam splitter 459A, reflected by mirror 459B, and then reflected by beam-steering mirror 452 as reference beam 434. Reference beam 434 is reflected by polarizing beam splitter 466B as the reference beam component of beam 435.

The description first output beam 438, detector 476, and signal 444 is the same as corresponding portions of the description given of beam 638, detector 676, and signal 644 of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

Interferometer system 400 and stage mirror 462 introduce a phase shift φ₆ between the measurement and reference beam components of the second output beam 440 and mixed output beam 442. A detector 480 measures the intensity of mixed output beam 442, e.g., preferably by photoelectric detection, to produce electrical interference signal or electrical heterodyne signal s₆. Heterodyne signal s₆ is transmitted to electronic processor and computer 482 in either digital or analog format, preferably in digital format. Electronic processor and computer 482 extracts the phase of heterodyne signal s₆, determines phase φ₆ from the phase, and determines from phase φ₆ an orientation angle θ₆ of measurement object mirror 462. Angle θ₆ is an orientation of a normal to the reflecting surface of measurement object mirror 462 relative to a selected reference line in the plane of FIG. 5a and is computed using the formula $\begin{matrix} {{\theta_{6} = {{2{\arctan \quad\left\lbrack \frac{\eta_{6}}{1 + \eta_{6}} \right\rbrack}} - {\int{\left( \frac{\partial n}{\partial r} \right)\quad {s}}}}}{where}} & (15) \\ {{\eta_{6} = \left\lbrack \frac{\phi_{6}}{2n_{M}{ka}} \right\rbrack},} & (16) \end{matrix}$

the integration is along the coextensive optical paths of the reference and measurement beams comprising a gas, and (∂n/∂s) is the partial derivative of the refractive index of the optical path at a respective point along the coextensive reference and measurement beam paths with respect to a vector orthogonal to the optical path of the measurement and reference beams and parallel to the plane of FIG. 5c.

The classification of the fifth embodiment as comprising an angular displacement interferometer operating in an angular displacement mode, a non-null mode, is a result of the procedure wherein the phase φ₆ is not servoed to a zero value and is a direct measure of the relative orientation of the measurement object mirror as a function of time.

The remaining description of the fifth embodiment is the same as corresponding portions of the description given for the second embodiment of the present invention and the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

A variant of the fifth embodiment of the present invention from the first set of embodiments is shown schematically in FIGS. 5c-5 g comprising two interferometers and a dynamic beam-steering assembly for a measurement of an orientation of an object, e.g., a stage mirror, in two orthogonal planes. A first interferometer measures changes in the orientation of measurement object mirror 462 in the plane of FIG. 5c and a second interferometer measures changes in the orientation of measurement object mirror 462 in a plane parallel to beam 431 and orthogonal to the plane of FIG. 5c. The beam-steering assembly is configured with transducers and a support structure for the associated beam-steering mirror appropriate for control the angular orientation of the beam-steering mirror in two orthogonal planes.

The first interferometer comprises the interferometer of the fifth embodiment of the present invention and beam splitter assemblies 490 and 492 shown in FIGS. 5c, 5 e, and 5 f. The planes of FIGS. 5e and 5 f are orthogonal to the plane of FIG. 5c. A portion of measurement beam 433 is transmitted by polarizing interface 490A (see FIG. 5e). A portion of the reference beam reflected by mirror 459B is transmitted by non-polarizing interface 492A as reference beam 434 (see FIG. 5f). The net effect of beam splitter assemblies 490 and 492 on the first interferometer is to decrease the magnitude of the measurement and reference beam components of beam 435 preferably by approximately the same factor. The remaining description of the first interferometer is the same as corresponding portions of the description given for the fourth embodiment.

The second interferometer comprises elements of the first interferometer up through beam-steering mirror for the measurement beam, up through mirror 459B for the reference beam, and elements shown in FIG. 5g. A second portion of the measurement beam 433 is reflected by non-polarizing interface 490A and then reflected by polarizing interface 490 B as a measurement beam component of a third output beam 440A. (see FIGS. 5e and 5 g) The planes of FIGS. 5c and 5 g are separated by a distance b as shown in FIGS. 5e and 5 f. A second portion of the reference beam incident on beam-splitter assembly 492 is reflected by non-polarizing interface 492A as a second reference beam and then reflected by surface 492B (see FIG. 5f). The second reference beam exiting beam-splitter assembly 492 is incident on rhomb 494 and after two internal reflections by surfaces 494A and 494B, is reflected by beam-steering mirror 452 as reference beam 434A. Reference beam 434A and measurement beam 433 lie in the plane of FIG. 5e that is preferably orthogonal to the planes of FIGS. 5c and 5 g. Reference beam 434A is incident on beam-splitter assembly 490 and transmitted by polarizing interface 490B as the reference beam component of the third output beam 440A.

Third output beam 440A is transmitted by a polarizer 478A as a mixed output beam 442A (see FIG. 5g). The second interferometer and measurement object mirror 462 introduce a phase shift φ_(6A) between the measurement and reference beam components of the third output beam 440A and mixed output beam 442A. A detector 480A measures the intensity of mixed output beam 442A, e.g., preferably by photoelectric detection, to produce electrical interference signal or electrical heterodyne signal s_(6A). Heterodyne signal s_(6A) is transmitted as electronic signal 446A, preferably in digital format, to electronic processor and computer 482A. Electronic processor and computer 482A extracts the phase from heterodyne signal s_(6A), determines phase φ_(6A) from the phase, and determines the orientation angle θ_(6A) from phase φ_(6A) by the same procedures and corresponding equations as used by electronic processor and computer 482, with parameter a replaced by parameter b, to extract the phase of heterodyne signal s₆ and determines the orientation angle θ₆. The orientation angle θ_(6A) indicates the orientation of normal to the surface of measurement object mirror 462 relative to a selected reference line, both the normal and the reference line lying in a plane defined by the plane of the second measurement and reference beams.

The remaining description of the variant of the fifth embodiment is the same as corresponding portions of the description given for the fifth embodiment of the present invention.

A sixth embodiment of the present invention is shown schematically in FIGS. 6a and 6 b comprising an interferometer system and a dynamic beam-steering assembly for an orientation measurement of an object, e.g., a stage mirror. The sixth embodiment is from the first set of embodiments comprising two linear displacement interferometers arranged to make angular displacements operating in non-null or displacement mode. The sixth embodiment is further of the second system type, the same system type as the second and fifth embodiments of the present invention, wherein a beam-steering assembly redirects the measurement beams of the linear displacement interferometer.

A number of the elements of the sixth embodiment perform like functions as elements of the sixth embodiment described in U.S. patent application having Ser. No. 09/157,131. The element numbers of elements in FIGS. 6a and 6 b performing like functions in the sixth embodiment are 100 less than the element numbers of the corresponding elements of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

The description of input beam 510 in FIG. 6a is the same as the description of input beam 14 of the first embodiment of the present invention. The description of measurement beams 511 through measurement beam 531 is the same as corresponding portions of the description given for measurement beams 611 through measurement beam 631 of the sixth embodiment in U.S. patent application having Ser. No. 09/157,131. A portion of measurement beam 531 is transmitted by non-polarizing beam splitter 559A and reflected by beam-steering mirror 552 as a first measurement beam 533. First measurement beam 533 is reflected by mirror 566A as first measurement beam 535. First measurement beam 535 is reflected by polarizing beam splitter 572 as a measurement beam component of beam 536. A second portion of measurement beam 531 is reflected by non-polarizing beam splitter 559A, reflected by mirror 559B, and then reflected by beam-steering mirror 552 as a second measurement beam 534. As shown in FIG. 6a, first and second measurement beams 533 and 534 are separated by a distance a. Second measurement beam 534 is reflected by mirror 566B as second measurement beam 539. Second measurement beam 539 is reflected by polarizing beam splitter 575 as a measurement beam component of a third output beam 541.

A portion of reference beam 516, as shown in FIG. 6a, is first transmitted by non-polarizing beam splitter 571 and then transmitted by polarizing beam splitter 572 as a reference beam component of beam 536. A second portion of reference beam 516 is reflected by non-polarizing beam splitter 571, reflected by mirror 573, and then transmitted by polarizing beam splitter 575 as a reference beam component of the third output beam 541.

A portion of beam 536 is reflected by non-polarizing beam splitter 574 as a first output beam 538. The description first output beam 538, detector 576, and signal 544 is the same as corresponding portions of the description given of beam 438, detector 476, and signal 444 of the fifth embodiment of the present invention.

A second portion of beam 536 is transmitted by non-polarizing beam splitter 574 as a second output beam 540. Second output beam 540 is transmitter by analyzer 578 as mixed second output beam 542, the polarization states of the reference beam component and the measurement beam component of the mixed second output beam being the same. Third output beam 541 is transmitted by analyzer 579 as mixed third output beam 543, the polarization states of the reference beam component and the measurement beam component of the mixed third output beam being the same.

Interferometer system 500 and measurement object mirror 562 introduce phase shifts φ₇ and φ₈ between the measurement and reference beam components of mixed second and third output beams 542 and 543, respectively. Detectors 580 and 581 measure the intensities of mixed second and third output beams 542 and 543, respectively, e.g., preferably by photoelectric detection, to produce electrical interference signals or electrical heterodyne signals s₇ and s₈, respectively. Heterodyne signals s₇ and s₈ are transmitted to electronic processor and computer 582 as signals 546 and 547, respectively, in either digital or analog format, preferably in digital format. Electronic processor and computer 582 extracts the phases of heterodyne signals s₇ and s₈, determines phases φ₇ and φ₈ from the extracted phases, and determines from the phase difference φ₈−φ₇ an orientation angle θ₇ of stage mirror 562. Angle θ₇ is an orientation of a normal to the reflecting surface of measurement object mirror 462 relative to a selected reference line in the plane of FIG. 6a and is computed using the formula $\begin{matrix} {{\theta_{7} = {{2{\arctan \quad\left\lbrack \frac{\eta_{7}}{1 + \eta_{7}} \right\rbrack}} - {\int{\left( \frac{\partial n_{M}}{\partial r} \right)\quad {s}}}}}{where}} & (17) \\ {{\eta_{7} = \left\lbrack \frac{\phi_{8} - \phi_{7}}{2n_{M}{ka}} \right\rbrack},} & (18) \end{matrix}$

the integration is along the optical path of the measurement beam comprising the gas, and (∂n_(M)/∂s) is the partial derivative of the refractive index of the optical path comprising the gas at a respective point along the measurement path with respect to a vector orthogonal to the optical path of the measurement beam and parallel to the plane of FIG. 6a.

The classification of the sixth embodiment as two linear displacement interferometers operating in an angular displacement mode, a non-null mode, is a result of the procedure wherein the difference in phase φ₈−φ₇ is not servoed to a zero value and is a direct measure of the relative orientation of the measurement object mirror as a function of time.

The remaining description of the sixth embodiment is the same as corresponding portions of description given for the second and fifth embodiments of the present invention and the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

A variant of the sixth embodiment of the present invention is shown schematically in FIGS. 6c-6 g comprising three interferometers and a dynamic-beam steering assembly for a measurement of the orientation of an object, e.g., a stage mirror in two orthogonal planes. A combination of two of the three interferometers measures changes in orientation of measurement object mirror 562 in the plane of FIG. 6c and a second combination of two of the three interferometers measures changes in orientation of measurement object mirror 562 in a plane parallel to beam 531 and orthogonal to the plane of FIG. 6c.

The first combination of interferometers comprises the two interferometers of the sixth embodiment of the present invention and beam splitter assemblies 590 and 592 shown in FIGS. 6c, 6 e, and 6 f. The plane of FIGS. 6e and 6 f are orthogonal to the plane of FIG. 6c. A portion of the portion of measurement beam 531 transmitted by non-polarizing beam splitter 559A is transmitted by non-polarizing interface 590A (see FIG. 6e). A portion of the portion of reference beam 516 transmitted by non-polarizing beam splitter 571 is transmitted by non-polarizing interface 592A as a reference beam (see FIG. 6f). The net effect of beam splitter assemblies 590 and 592 on the first combination of two interferometers is to decrease the magnitude of the measurement and reference beam components of beam 536 preferably by approximately the same factor. The remaining description of the first combination of two interferometers is the same as corresponding portions of the description given for the two interferometers of the fifth embodiment of the present invention.

The second combination of two interferometers comprises one of the interferometers of the first combination of two interferometers and a second interferometer. The second interferometer of the second combination of two interferometers comprises elements of the first combination of two interferometers up through non-polarizing beam-steering 559A for the measurement beam, up through non-polarizing beam splitter 571 for the reference beam, and elements shown in FIG. 6g. A second portion of the portion of measurement beam 531 transmitted by non-polarizing beam splitter 559A is reflected by non-polarizing interface 590A, reflected by reflecting surface 590B, and then reflected by beam-steering mirror 552 as a measurement beam 533A (see FIG. 6g). Beam 533A is reflected by mirror 566C and then reflected by polarizing beam-splitter 572A as a measurement beam component of third output beam 540A (see FIG. 6g). A second portion of the portion of reference beam 516 transmitted by non-polarizing beam-splitter 571 is reflected by non-polarizing interface 592A, reflected by reflecting surface 592B, and then transmitted polarizing beam splitter 572A as a reference beam component of third output beam 540A (see FIG. 6g). Measurement beam 533A and measurement beam 533 lie in the plane that is preferably orthogonal to the planes of FIGS. 6c and 6 g and separated by a distance b (see FIG. 6e.

Third output beam 540A is transmitted by a polarizer 578A as a mixed output beam 542A (see FIG. 6g). The second interferometer of the second combination of two interferometers and measurement object mirror 562 introduce a phase shift φ₉ between the measurement and reference beam components of the third output beam 540A and mixed output beam 542A. A detector 580A measures the intensity of mixed output beam 542A, e.g., preferably by photoelectric detection, to produce electrical interference signal or electrical heterodyne signal s₉. Heterodyne signal s₉ is transmitted as electronic signal 546A, preferably in digital format, to electronic processor and computer 582A. Electronic processor and computer 582A extracts the phase of heterodyne signal s₉, determines φ₉ from the extracted phase, and transmits phase φ₉ as signal 583A preferably in digital format to processor 584.

Phase φ₇ is transmitted as signal 583 to processor 584 and processor 584 determines from phases φ₇ and φ₉ the phase difference φ₉−φ₇, an orientation angle θ_(7A) by the same procedures and equations corresponding equations as used by electronic processor and computer 582 with parameter a replaced by parameter b to determine from phases φ₇ and φ₈ an orientation angle θ₇. Orientation angle θ_(7A) indicates the orientation of the measurement object mirror 562 in a plane defined by the plane of measurement beam 531 and the measurement beam reflected by reflecting surface 590B.

The beam-steering assembly of the variant of the sixth embodiment is configured with transducers and a supporting arrangement for the beam-steering mirror of the beam-steering assembly appropriated for servo control of the orientation of the beam-steering mirror in two orthogonal planes.

The remaining description of the variant of the sixth embodiment is the same as corresponding portions of the description given for the sixth embodiment of the present invention.

A seventh embodiment of the present invention is shown schematically in FIGS. 7a-7 c comprising an interferometer system and a dynamic beam-steering assembly for a linear displacement and an orientation measurement of an object, e.g., a stage mirror. The seventh embodiment is from the second set of embodiments comprising a linear displacement interferometer and an angular displacement interferometer, the angular displacement interferometer operating in a null or differential mode, with the beam-steering assembly redirecting the measurement beams of the linear and angular displacement interferometers.

The seventh embodiment is of the second system type, the same system type as the second, fifth, and sixth embodiments of the present invention. The interferometer system comprises a linear displacement and an angular displacement measuring interferometers wherein the two interferometers measure a distance to a position on the surface of the object and a change in orientation of the object about the same position. The detected change in orientation is in a plane defined by the properties of the angular displacement interferometer.

A number of the elements of the seventh embodiment perform like functions as elements of the sixth embodiment of the present invention. Element numbers of elements in interferometer system 600 shown in FIGS. 7a and 7 b performing like functions in the seventh embodiment are 100 more than the element numbers of the corresponding elements of the sixth embodiment except for the location of elements 659A and 659B and properties of beam 634. FIG. 7b is in a plane orthogonal to that of FIG. 7a.

The description of input beam 610 in FIG. 7a is the same as the description of input beam 14 of the first embodiment of the present invention. The description of measurement beams 611 through measurement beam 631 is the same as corresponding portions of the description given for measurement beams 511 through measurement beam 531 of the sixth embodiment of the present invention. Measurement beam 631 is reflected by beam-steering mirror 652 as measurement beam 633. A first portion of measurement beam 633 is reflected by non-polarizing beam splitter 659A as a first measurement beam 635. First measurement beam 635 is reflected by polarizing beam splitter 672 as a measurement beam component of first output beam 640.

A second portion of measurement beam 633 is transmitted by non-polarizing beam splitter 659A and then reflected by mirror 659B as a measurement beam 634. A first portion of measurement beam 634 is reflected by non-polarizing beam splitter 673B and then transmitted by halfwave phase retardation plate 678 as a second measurement beam 641A. Halfwave phase retardation plate 678 is orientated so as to rotate the plane of polarization of beam 641A parallel to the plane of FIG. 7a. A second portion of measurement beam 634 is transmitted by non-polarizing beam splitter 673A and then reflected by mirror 673B as a third measurement beam 641B. As shown in FIG. 7a, the second and third measurement beams are separated by a distance a.

A portion of reference beam 616, as shown in FIG. 7a, is transmitted by polarizing beam splitter 672 as a reference beam component of output beam 640. Output beam 640 is transmitter by analyzer 678 as mixed output beam 642, the polarization states of the reference beam component and the measurement beam component of the mixed output beam being the same.

Interferometer system 600 and measurement object mirror 662 introduce phase shifts φ₁₀ and φ₁₁ between the measurement and reference beam components of mixed output beam 642 and the second and third measurement beams 641A and 641B, respectively. Detector 680 measures the intensity of mixed output beam 642, e.g., preferably by photoelectric detection, to produce electrical interference signal or electrical heterodyne signal s₁₀. Heterodyne signal s₁₀ is transmitted to electronic processor and computer 682H as signals 646, in either digital or analog format, preferably in digital format. As described further below, phase φ₁₀ can be analyzed to calculate changes in distance to measurement object mirror 682. Phase φ₁₁ can be used to provide a servo signal to reorient beam steering mirror 652 in response to changes in the angular orientation of measurement object mirror 682, which will is now described.

Second measurement beam 641A is incident on lens 681A of detector 681H and focused to a spot (see FIG. 7c). Second measurement beam 641A diverges from the spot whereupon it is sequentially reflected by mirrors 681E and 681D and then incident on non-polarizing beam splitter 681C. A first portion and a second portion of second measurement beam incident on non-polarizing beam splitter 681C are transmitted and reflected as second measurement beam components, respectively, of beams 643A and 643B, respectively.

Third measurement beam 641B is incident on lens 681A of detector 681H and focused to the spot. Third measurement beam 641B diverges from the spot whereupon it is reflected by mirror 681B and then incident on non-polarizing beam splitter 681C. A first portion and a second portion of third measurement beam incident on non-polarizing beam splitter 681C are reflected and transmitted as third measurement beam components, respectively, of beams 643A and 643B, respectively.

Beam 643A is transmitted by polarizer 679B as a second mixed beam. Beam 643B is transmitted by quarterwave phase retardation plate 679C and polarizer 679D as a third mixed beam. Quarter wave phase retardation plate 679C is orientated so as to introduce a 90° phase shift between the second and third measurement beam components of beam 643B. Detectors 685A and 685B measure the intensities of the second and third mixed beams, e.g., preferably by photoelectric detection, to produce electrical interference signals 647A and 647B, respectively, or electrical homodyne signals s_(11A) and s_(11B), respectively. Homodyne signals S_(11A) and s_(11B), are transmitted to electronic processor and computer 682H as signals 646 and 647, respectively, in either digital or analog format, preferably in digital format. Electronic processor and computer 682H extracts phase φ₁₁ from the in quadrature homodyne signals s_(11A) and s_(11B) using standard homodyne interferometry techniques known in the art.

Phase φ₁₁ is related to the angle of incidence δθ₁₁ of corresponding measurement beams on measurement object mirror 662. Angle δθ₁₁ is computed using the formula $\begin{matrix} {{{\delta\theta}_{11} = {{2{\arctan \quad\left\lbrack \frac{\eta_{11}}{1 + \eta_{11}} \right\rbrack}} - {\int{\left( \frac{\partial n_{M}}{\partial r} \right)\quad {s}}}}}{where}} & (19) \\ {{\eta_{11} = \left\lbrack \frac{\phi_{11}}{2n_{M}{ka}} \right\rbrack},} & (20) \end{matrix}$

the integration is along the optical path of the measurement beam comprising the gas, and (∂n_(M)/∂s) is the partial derivative of the refractive index of the optical path comprising the gas at a respective point along the measurement path with respect to a vector orthogonal to the optical path of the measurement beam and parallel to the plane of FIG. 7a.

The classification of the seventh embodiment as comprising an angular displacement interferometer operating in a null mode or differential mode is a result of the procedure wherein phase φ₁₁ is servoed to a zero value.

Signal processor and computer 682H transmits an error signal to servo controller 676H, based on the measured error δθ₁₁, and server controller 676H sends servo control signal 644H to translators 653A and 653B. The description of the servo control operation is the same as corresponding portions of the description given for the first embodiment. An angle measuring system 687 calculates the change in angular orientation of measurement object mirror 662 based on the change in angular orientation of beam-steering mirror 652. In the presently described embodiment, the angle measuring system directly measures the change in orientation of beam steering mirror 652 by using, for example, calibrated capacitance gauges. Alternatively, in other embodiments, the angle measurement system includes calibration data for beam-steering mirror 652 that correlates the servo control signal 644H to transducers 653A and 653B with a corresponding change in angular orientation of the beam steering mirror 652, which is directly related to the change in angular orientation of measurement object mirror 662 as described above.

In other embodiments, a frequency offset can be introduced between beams 641A and 641B by passing one of the beams through, for example, an electo-optic modulator or an acousto-optic modulator, or by dithering a mirror such as mirror 673A or 673B with a piezoelectric transducer. As a result, these beams, which have orthogonal linear polarizations, will produce a heterodyne signal s₁₁ from which electronic processor and computer 682H can determine φ₁₁. In further embodiments, second measurement beam 634 can be mixed with a reference beam portion separated from reference beam 616 to produce heterodyne signal s₁₁. In this case, the interferometer directs measurement beam 634 and the reference beam portion to propagate parallel to one another and to be spatially separated from one another by the distance a. Thereafter, a lens focuses them to a common spot on a detector where they interfere to produce heterodyne signal s₁₁.

The remaining description of the seventh embodiment is the same as corresponding portions of description given for the first, fourth, fifth, and sixth embodiments of the present invention and the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

The seventh embodiment reorients the beam steering mirror based on homodyne interferometric signals s_(11A) and s_(11B) (or on a heterodyne interferometric signal s₁₁), in contrast to, for example, measuring the spatial separations or differences in propagation directions between exit beams as in the embodiment of FIG. 6a. In a further variant, the embodiment of FIG. 6a can be modified to include an interferometric control system as in the seventh embodiment. Such a variant includes the components in FIG. 7a that are downstream from beam 634 and subjects beam 535 in FIG. 6a to those downstream components rather than the corresponding downstream components in FIG. 6a. Similarly, the two-dimensional variant corresponding to FIG. 6c can be modified to include an interferometric control system by subjecting beam 535 in FIG. 6c to the components downstream from beam 634 in FIGS. 7d and 7 f, which are now described below.

A variant of the seventh embodiment of the present invention is shown schematically in FIGS. 7d-7 f comprising an interferometer system and a dynamic-beam steering assembly for a measurement of an error in orientation of an object, e.g., a stage mirror, in two orthogonal planes. The planes of FIGS. 7e and 7 f are orthogonal to the plane of FIG. 7d. The interferometer system comprises three interferometers. One interferometer measures a linear displacement of measurement object mirror 662, a second interferometer of the three interferometers measures errors in orientation of measurement object mirror 662 in the plane of FIG. 7d, and a third interferometer of the three interferometers measures errors in orientation of measurement object mirror 662 in a plane parallel to beam 631 and orthogonal to the plane of FIG. 7d.

The first interferometer of the three interferometers is the same as the interferometer of the seventh embodiment that measures phase φ₁₀. The second interferometer of the three interferometers is the same the interferometer of the seventh embodiment that measures phase φ₁₁ with non-polarizing beam splitter 673A and mirror 673B replaced by non-polarizing beam splitters 673C and 673D, respectively.

Description of the third interferometer of the three interferometers is the same as corresponding portions of the description given for the second interferometer of the three interferometers up through beam 634. A portion of beam 634 is transmitted by non-polarizing beam splitters 673C and 673D as beam 641V shown schematically in FIG. 7f. As shown in FIG. 7f, beam 641V is incident on non-polarizing beam splitter 675A of detector 681V and a transmitted portion thereof is incident on halfwave phase retardation plate 679E and transmitted as a fourth measurement beam 641E. Halfwave phase retardation plate 679E is orientated so as to rotate the plane of polarization of beam 641E orthogonal to the plane of FIG. 7f and parallel to the plane of FIG. 7d. A second portion of beam 641V is reflected by non-polarizing beam splitter 675A and then reflected by mirror 675B as a fifth measurement beam 641F. Beam 641F is polarized parallel to the plane of FIG. 7f and beams 641E and 641F are separated by a distance b (see FIG. 7f). The remaining elements of detector 681V are the same as corresponding elements of detector 681H.

Fourth and fifth measurement beams 641E and 641F propagate through respective elements of detector 681V to form beams 643C and 643D. Beam 643C is transmitted by polarizer 679B as a fourth mixed beam. Beam 643D is transmitted by quarterwave phase retardation plate 679C and polarizer 679D as a fifth mixed beam. Quarterwave phase retardation plate 679C is orientated so as to introduce a 90° phase shift between the fourth and fifth measurement beam components of beam 643D. Detectors 685A and 685B of detector 681V measure the intensities of the fourth and fifth mixed beams, e.g., preferably by photoelectric detection, to produce electrical interference signals 647C and 647D, respectively, or electrical homodyne signals s_(12A) and s_(12B), respectively.

The third interferometer of the three interferometers and measurement object mirror 662 introduces a phase shift φ₁₂ between fourth and fifth measurement beams 641E and 641F. Homodyne signals s_(12A) and s_(12B) are transmitted as electronic signals 647C and 647D, preferably in digital format, to electronic processor and computer 682HV as signal 647V. Electronic processor and computer 682HV extracts phase φ₁₂ from homodyne signals s_(12A) and s_(12B). Phase φ₁₂ is related to the angle of incidence δθ₁₂ of corresponding measurement beams on measurement object mirror 662. Angle δθ₁₂ is computed using Eqs. (19) and (20) with δθ₁₂ corresponding to δθ₁₁, φ₁₂ corresponding to φ₁₁, η₁₂ corresponding to η₁₁, and b corresponding to a.

The orientation angle δθ₁₂ indicates an error in orientation of the stage mirror 662 in a plane defined by the plane of measurement beams 641E and 641F projected by beam-steering mirror 652 on stage mirror 662, a plane that is orthogonal to the plane of FIG. 7d and parallel to beam 631 in FIG. 7d. Signal processor and computer 682HV transmits error signals to servo controller 676HV, based on the measured errors δθ₁₁ and δθ₁₂, and server controller 676HV sends servo control signal 644HV comprising two components to translators 653A and 653B and a third translator (not shown in a figure). The description of the servo control operation is the same as corresponding portions of the description given for the first embodiment.

The remaining description of the variant of the seventh embodiment is the same as corresponding portions of the description given for the seventh embodiment of the present invention and for the variant of the sixth embodiment of the present invention.

An eighth embodiment of the present invention is shown schematically in FIGS. 8a-8 c comprising an interferometer system and a dynamic beam-steering assembly for an orientation measurement of an object, e.g., a stage mirror. The eighth embodiment is from the first set of embodiments comprising two linear displacement measuring interferometers, configured to measure an angular displacement, operating in non-null or displacement mode. In addition, a beam-steering assembly is separate from the interferometer system and redirects both an input beams to and output beams from the interferometer system and reference and measurement objects.

The eighth embodiment is shown schematically in FIGS. 8a-8 c. The eighth embodiment comprises an interferometer with a beam-steering assembly redirecting both input and outpur beams by a beam-redirecting element in a manner to not be sensitive in first order to a linear displacement of the beam-redirecting element. The redirection of both input and output beams of an interferometer by a beam-redirecting element in the manner is feature of a third system type. The third system type further comprises the reflection of the measurement beams by the measurement object mirror where, at the measurement object mirror, the measurement beams are substantially parallel and coextensive.

A number of the elements of the eighth embodiment perform like functions as elements of the thirteenth embodiment described in U.S. patent application having Ser. No. 09/157,131 and schematically shown therein in FIGS. 13a and 13 b. The element numbers of elements in FIGS. 8a-8 c performing like functions in the eighth embodiment are 600 less than the element numbers of corresponding elements of the thirteenth embodiment in U.S. patent application having Ser. No. 09/157,131.

The description of input beam 710 in FIG. 8a is the same as the description of input beam 14 of the first embodiment of the present invention. The description of measurement beam component of beam 712 and subsequent measurement beam components or measurement beams up through and including measurement beam 723 is the same as corresponding portions of the description given for the measurement beam component of beam 1312 and subsequent measurement beam components or measurement beams up through and including measurement beam 1323 of the thirteenth embodiment in U.S. patent application having Ser. No. 09/157,131.

A portion of measurement beam 723 is transmitted by non-polarizing beam splitter 768A, reflected by polarizing beam splitter 768B, and then reflected by mirror 770A as a measurement beam component of output beam 730A of the first interferometer. A second portion of measurement beam 723 is reflected by non-polarizing beam splitter 768A, reflected by mirror 770A, reflected by polarizing beam splitter 770B, and then reflected by mirror 770A as a measurement beam component of output beam 730B of the second interferometer. The separation of the portion of measurement beam 723 transmitted by non-polarizing beam splitter 768A and the second portion of measurement beam 723 reflected by non-polarizing beam splitter 768A and reflected by mirror 770A is shown on FIG. 8a as a separation a.

A portion of reference beam 720 is transmitted by non-polarizing beam splitter 768C, transmitted by polarizing beam splitter 768B, and then reflected by mirror 770A as a reference beam component of output beam 730A of the first interferometer. A second portion of reference beam 720 is reflected by non-polarizing beam splitter 768C, reflected by mirror 768D, transmitted by polarizing beam splitter 770B, and then reflected by mirror 770A as a reference beam component of output beam 730B of the second interferometer.

The description of the generation of a first output beam 740A and a second output beam 744A from output beam 730A of the first interferometer is the same as corresponding portions of the description given for the generation of an output beam 1340 and an output beam 1344 from output beam 1330, respectively, of the thirteenth embodiment in U.S. patent application having Ser. No. 09/157,131, certain elements of the ninth embodiment performing like functions of elements of the thirteenth embodiment in U.S. patent application having Ser. No. 09/157,131. The alphanumeric numbers of the certain elements comprise a suffix A and a numeric component 600 less than the numbers of elements performing the same functions in the thirteenth embodiment in U.S. patent application having Ser. No. 09/157,131. The description of a generation of a third output beam 744B from output beam 730B of the second interferometer is the same as corresponding portions of the description given for the generation of output beam 744A from output beam 730A of the first interferometer, certain other elements of the second interferometer performing like functions of elements of the first embodiment. Alphanumeric numbers of the certain other elements are the same as the alphanumeric numbers of elements performing the like functions in the first interferometer except for the change of suffixes A to suffixes B. In the second interferometer, there is no element corresponding to non-polarizing beam splitter 782A.

The description of first output beam 740A, detector 784A, and signal 748A is the same as corresponding portions of the description given of beam 1340, detector 1384, and signal 1348 of the thirteenth embodiment in U.S. patent application having Ser. No. 09/157,131. The description second output beam 740B, detector 784B, and signal detector and processor 748B is the same as corresponding portions of the description given of beam 740A, detector 784A, and signal detector and processor 748A of the eighth embodiment of the present invention.

The first and second interferometers and measurement object mirror 760 introduce a phase shifts φ₁₃ and φ₁₄, respectively, between the measurement and reference beam components of mixed second and third output beams 746A and 746B, respectively. Detectors 788A and 788B measure the intensities of mixed second and third output beams 746A and 746B, respectively, e.g., preferably by photoelectric detection, to produce electrical interference signals or electrical heterodyne signals s₁₃ and s₁₄, respectively. Heterodyne signals s₁₃ and s₁₄ are transmitted to electronic processor and computers 790A and 790B, respectively, as signals 746A and 746B, respectively, in either digital or analog format, preferably in digital format. Electronic processor and computers 790A and 790B extract phases φ₁₃ and φ₁₄, respectively, of heterodyne signals s₁₃ and s₁₄, respectively. Phases φ₁₃ and φ₁₄ are transmitted as signals 747A and 747B, respectively to processor 790. Processor 790 determines from phases φ₁₃ and φ₁₄ a phase difference φ₁₄−φ₁₃ and from phase difference φ₁₄−φ₁₃, determines a angle θ₁₃ of an orientation of measurement object mirror 760. Angle θ₁₃ is an orientation of a normal to the reflecting surface of measurement object mirror 760 in the plane of FIG. 8a and is computed using the formula $\begin{matrix} {{\theta_{13} = {{2{\arctan \quad\left\lbrack \frac{\eta_{13}}{1 + \eta_{13}} \right\rbrack}} - {\int{\left( \frac{\partial n_{M}}{\partial r} \right)\quad {s}}}}}{where}} & (19) \\ {{\eta_{13} = \left\lbrack \frac{\left( {\phi_{14} - \phi_{13}} \right)}{2n_{M}{ka}} \right\rbrack},} & (20) \end{matrix}$

the integration is along the optical path of the measurement beam comprising the gas and (∂n_(M)/∂s) is the partial derivative of the refractive index of the optical path comprising the gas at a respective point along the measurement path with respect to a vector orthogonal to the optical path of the measurement beam and parallel to the plane of FIG. 8a.

The remaining description of the eighth embodiment is the same as corresponding portions of the description given for the sixth embodiment of the present invention.

A variant of the eighth embodiment is described comprising an interferometer system and a dynamic-beam steering assembly for a measurement of the orientation of an object, e.g., a stage mirror in two orthogonal planes. The interferometer system of the variant of the eighth embodiment comprises an interferometer system the same as the interferometer system of the eighth embodiment and the addition of a third interferometer to the interferometer system of the eighth embodiment in a manner the same as the manner as the second interferometer of the sixth embodiment is added to the first interferometer of the sixth embodiment. The remaining description of the variant of the eighth embodiment is the same as corresponding portions given for the description of the sixth embodiment, the variant of the sixth embodiment, and eighth embodiment of the present invention.

A ninth embodiment of the present invention is shown schematically in FIGS. 11a-11 e comprising an interferometer system and a dynamic beam-steering assembly for a linear displacement and an orientation measurement of an object, e.g., a stage mirror. The ninth embodiment is from the second set of embodiments comprising a linear displacement interferometer and angular displacement interferometer, the angular displacement interferometer operating in a null or differential mode, with the beam-steering assembly redirecting the measurement beams of the linear and angular displacement interferometers.

The ninth embodiment is of the same system type, the second system type, as the second, fifth, sixth, and seventh embodiments of the present invention. The interferometer system comprises a linear displacement and an angular displacement measuring interferometers wherein the two interferometers measure a distance to a position on the surface of the object and a change in orientation about the same position. The detected change in orientation is in a plane defined by the properties of the angular displacement interferometer.

The ninth embodiment of the present invention relates to polarization preserving optical systems and their use as components in linear and angular displacement measuring interferometers. Each polarization preserving optical system incorporated in the ninth embodiment comprises two properties. The first property is that for such an optical system, there exists a set of orientations of planes of linear polarization of an input beam to the optical system for which the polarization state of the input beam at each reflecting and refracting surface of the optical system and a corresponding output beam are all linear. The set of planes of linear polarization orientations hereinafter will be referred to as eigenmodes. Thus, the optical systems “preserve”, for an input beam to the system having an eigenmode state of linear polarization, the linear state of polarization of the input beam at each reflecting and refracting surface of the optical system and the corresponding output beam.

A set of the optical systems that exhibit such eigenmodes comprise reflecting and refracting surfaces such that the plane of polarization of an eigenmode at each of any reflecting or refracting surface in the optical system is either parallel to or orthogonal to the plane of incidence at the surface. The propagation direction of an incident ray and its linear polarization define the plane of polarization. The normal to a given surface and the propagation direction of the incident ray define the plane of incidence for that surface and ray. A corner cube retroreflector is an example of an optical system that does not preserve exhibit such eigenmodes because any incident, linearly polarized ray will contact at least one surface of the corner cube such that the plane of polarization is neither orthogonal or parallel to the plane of incidence. Thus, linearly polarized beams emerge from corner cube retroreflectors with at least some polarization ellipticity.

In part because of the absence of a corner cube retroreflector, this first property (polarization preservation) is also present in the first, second, third, fourth, and fifth embodiments described previously.

The second property is that apparatus of the ninth embodiment further comprises optical systems having a certain set of transformation properties. The set of transformation properties describe a specific relationship between changes in the direction of propagation of an output beam from an optical system that results from changes in the direction of propagation an input beam wherein the directions of propagation of the input and output beams may or may not be parallel. A corner cube retroreflector is an example of an optical system exhibiting the set of transformation properties. The set of transformation properties will hereinafter be referred to as a transformation type T_(Ret). The set of transformation properties are opposite to those of a plane mirror. For example, as the angle of incidence on a plane mirror increase, the angle of reflection from the plane mirror increases, but in an opposite direction. In contrast, when the incident angle of an input ray into a corner cube retroreflector changes, the angle of the output ray changes in the same direction so as to maintain the input and output rays parallel to one another. Along with other interferometers utilizing polarization preserving optical systems, the interferometer system and a dynamic beam-steering assembly of the ninth embodiment is further described with respect to properties of polarization preserving optical systems and transformations of type T_(Ret) in copending, commonly owned U.S. patent application (Attorney Case Number 0202/US) entitled “Interferometers Utilizing Polarization Preserving Optical Systems” by Henry A. Hill and Peter J. de Groot and filed on the same date as the present application, the copending application being incorporated herein by reference.

The ninth embodiment comprises a differential plane mirror interferometer 1101 with a dynamic element 1155 as shown in diagrammatic perspective view in FIG. 11a. The orientation of dynamic element 1155 is servoed to maintain the measurement beam perpendicular to an object mirror 1153.

The description of input beam 1171 is the same as the corresponding portion of the description given for the source of input beam 14 of the first embodiment of the present invention. Input beam 1171 comprises two orthogonally polarized components having frequencies different one for the other. Input beam 1171 enters a first beam splitter comprising a right angle prism 1141 and a rhomboidal prism 1142 with a polarizing interface 1143. A first portion of input beam 1171 incident on polarizing interface 1143 is transmitted as a measurement beam 1173. A second portion of input beam 1171 incident on polarizing interface 1143 is reflected and exits the first beam splitter, after an internal reflection, as a reference beam 1174. Measurement beam 1173 then reflects from dynamic mirror 1155 to optical subsystem 1100, where as reference beam 1174 propagates directly to optical subsystem 1100. The orientation of dynamic mirror 1155 is controlled by transducers 1156A, 1156B, and 1156C. Propagation of these beams through optical subsystem 1100 is illustrated in FIG. 11a., and the details of optical subsystem 1100 will be described further below.

Measurement beam 1173 and reference beam 1174 exit subsystem 1100 as output measurement and reference beams 1175 and 1176, respectively. Output measurement and reference beams 1175 and 1176 are combined into a mixed output beam and a second output beam by a second beam splitter comprising right angle prisms 1144 and 1147, rhomboidal prism 1145, and beam splitting interfaces 1146 and 1148. The mixed and second output beams are received by detector and signal processors 1160 and 1161, respectively, that operate to provide information about linear and angular displacements of object mirror 1153 and information relating to the alignment of beams, e.g., such as detection of changes in direction of propagation of the second output beam, used for the servo control of dynamic mirror 1155.

The following coordinate system is defined for FIG. 11a, the y-axis is parallel to beams 1171, 1173, and 1174, the z-axis is parallel to beams 1175 and 1176, and the x-axis is perpendicular to the y- and z-axes. Upon exiting prism 1141, measurement beam 1173 is linearly polarized along the x-axis, and upon exiting rhomboidal prism 1142 reference beam 1174 is linearly polarized along the z-axis.

Optical subsystem 1100, quarter-wave phase retardation plate 1151, and reference mirror 1154 exhibit, as a first optical system, polarization preserving eigenmodes and the type T_(Ret) transformation properties for input reference beam 1174. Also, optical subsystem 1100, quarter-wave phase retardation plate 1151, object mirror 1153, and dynamic element 1155 for a fixed orientation exhibit, as a second optical system, polarization preserving eigenmodes and the type T_(Ret) transformation properties for input measurement beam 1174.

Optical subsystem 1100 comprises a modified Porro prism 1121 and prisms 1125, 1129, and 1133 shown schematically in FIGS. 11b, 11 c, 11 d, and 11 e, respectively. FIGS. 11b, 11 c, 11 d, and 11 e shows views of Porro prism 1121 and prisms 1125, 1129, and 1133, respectively, from each of the x-y, x-z, and y-z planes, with the particular plane specified by the coordinate axes to the left of the view. An interface comprising surfaces 1128 and 1130 is a polarizing beam splitter interface.

There are two polarization preserving eigenmodes of the first optical system wherein the input polarization states of the two eigenmodes are orthogonal and parallel, respectively, to the plane of incidence at surface 1136 of prism 1133. The corresponding output polarization states of the two polarization preserving eigenmodes are orthogonal and parallel to the plane of incidence at surface 1123 of prism 1121. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in the first optical system.

There are also two polarization preserving eigenmodes of the second optical system wherein the input polarization states of the two eigenmodes are orthogonal and parallel, respectively, to the plane of incidence at a first surface of dynamic element 1155. The plane of incidence at the first surface of dynamic element 1155 is parallel to the plane of incidence of beams of the eigenmodes at surface 1123 of Porro prism 1121. The corresponding output polarization states of the two polarization preserving eigenmodes are parallel and orthogonal, respectively, to the planes of incidence of a surface of dynamic element 1155. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in the second optical system.

The polarization preserving property is also present in the first, second, third, fourth, and fifth embodiments described previously.

The transformation properties of the first and second optical systems of the ninth embodiment with respect to changes in direction of propagation of output beams 1175 and 1176 that result from changes in direction of propagation of input beams 1173 and 1174, respectively, are the same as the properties of the type T_(Ret) transformation. For example, if the angle of incidence of measurement beam 1173 on dynamic mirror 1155 increases, the angle of reflection of output beam 1175 from dynamic mirror 1155 decreases.

The description of the detection and processing of the mixed beam by component 1160 is the same as the corresponding portion of the description of the detection and processing of beam 640 by analyzer 678, detector 680, and electronic processor and computer 682H of the seventh embodiment (see FIG. 7a). The description of the detection and processing of the second output beam by component 1161 is the same as the corresponding portion of the description of the detection and processing of beam 634 by non-polarizing beam splitter 673A, mirror 673B, halfwave phase retardation plate 679A, detector 681H, and electronic processor and computer 682H of the seventh embodiment (see FIG. 7a). The description of the control of transducers 1156A, 1156B, and 1156C of the ninth embodiment is the same as the corresponding portion of the description of the control of transducers 653A and 653B by servo controller 676 of the seventh embodiment (see FIG. 7a).

Alternatively, in another variant of the ninth embodiment, the processing can be similar to the sixth embodiment (see FIG. 6a). In particular, a beam splitting rhomb can be positioned before the measurement beam reflects from dynamic mirror 1155 to form output beam 1175, just as components 559A and 559B split beam 531 into two and direct them to dynamic mirror 552 in FIG. 6a. Thereafter, the processing of the two portions of the measurement beam that reflect from the dynamic mirror 1155 and of the reference output beam 1176 is identical to the processing of beams 533, 534, and 516, respectively, in the embodiment of FIG. 6a.

In a further variant of the ninth embodiment, the interferometry system only measures changes in distance to (and not changes in angular orientation of) object mirror 1153 based on an interferometric signal measured by component 1160. Component 1161 provides the servo information to reorient dynamic mirror 1155 based on a portion of measurement output beam 1175, which provides, e.g., spatial or interferometric information.

The remaining description of the ninth embodiment is the same as corresponding portions of description given for the first, fourth, fifth, sixth, and seventh embodiments of the present invention and the sixth embodiment in U.S. patent application having Ser. No. 09/157,131.

A variant of the ninth embodiment of the present invention is described that comprises an interferometer system and a dynamic-beam steering assembly for a measurement of an error in orientation of an object, e.g., a stage mirror, in two orthogonal planes. The description of the variant of the ninth embodiment is the same as the description of the ninth embodiment up through the detection and electronic processing of the second output beam. For the variant of the ninth embodiment, the description of the detection and processing of the second output beam by detector, electronic processor, and computer 1161 is the same as the corresponding portion of the description given for the detection and processing of beam 634 by non-polarizing beam splitters 673C and 673D, halfwave phase retardation plate 679A, detectors 681H and 681V, and electronic processor and computer 682HV of the variant of the seventh embodiment (see FIG. 7d). The description of the control of transducers 1156A, 1156B, and 1156C of the variant of the ninth embodiment is the same as the corresponding portion of the description given for the control of transducers 653A, 653B, and 653C (not shown) by servo controller 676HV of the variant of the seventh embodiment (see FIG. 7a).

The remaining description of the variant of the ninth embodiment is the same as corresponding portions of the description given for the ninth embodiment, the variant of the sixth embodiment, and the variant of the seventh embodiment of the present invention. The ninth embodiment and its variants provide a particularly compact arrangement for a dynamic distance and angle measuring interferometry system.

The first nine embodiments and variants thereof are based on modifications of certain embodiments of the U.S. patent application having Ser. No. 09/157,131. It will be apparent to those skilled in the art that other of the embodiments in U.S. patent application having Ser. No. 09/157,131 can also be used in a modified form to measure angular displacement using the techniques and procedures used in the first nine embodiments and variants thereof of the present invention for the generation of an angular displacement interferometer without departing from the scope and spirit of the present invention.

Embodiments from the second set of embodiments of the present invention are next described wherein each embodiment comprises at least one angular displacement interferometer and a linear displacement interferometer. The first of these embodiments, the tenth embodiment, comprises the interferometer system and beam-steering assembly of the second embodiment shown schematically in FIG. 2 except that detector and processor 180 performs additional functions. For the ninth embodiment, detector and processor 180 further computes the average phase, (φ₂+φ₃)/2, from phases φ₂ and φ₃, and calculates the difference in physical path length L between the measurement and reference paths based on the average phase, i.e., L=(φ₂+φ₃)/2nk , where k is the wavevector and n is the refractive index of the gas in the measurement path. For the tenth embodiment the measured value of L is sensitive to translations of beam steering mirror 160 in a direction normal to its reflective surface.

The line of reference for the measurement beam of the ninth embodiment is defined by the direction of measurement beam 118, a defined zero orientation of beam-steering mirror 160, and the relationship between locations of polarizing beam splitter 142, beam splitter assembly 144, and mirror 148. For example, with beam-steering mirror 160 at the zero orientation and the corresponding path length of beam 122 equal to one half of the corresponding path length of beam 125, the corresponding path of beam 120 defines the line of reference.

The line of measurement is defined by the path of beam 120, which intersects measurement object mirror 166 at normal incidence. The linear displacement represented by average phase (φ₂+φ₃)/2 is a displacement measured along the line of measurement. For the example given in the preceding paragraph, the line of measurement coincides with the line of reference and has a zero Abbé offset. Alternatively, a nonzero Abbé offset can be designed into the tenth embodiment by changing the location of polarizing beam splitter 142 relative the beam splitter assembly 144 and mirror 148.

The remaining description of the tenth embodiment is the same as corresponding portions of description given for the second embodiment. In other embodiments, similar distance calculations can be performed by detector and processor 180 based on only one of phases φ₂ and φ₃.

The second embodiment of the second set of embodiments, the eleventh embodiment, comprises the interferometer system and beam-steering assembly of the sixth embodiment shown schematically in FIGS. 6a and 6 b except that processor 582 performs additional functions. For the eleventh embodiment, processor 582 further calculates the difference in physical path length L between the measurement and reference paths based on φ₇, i.e., L=φ₇/2nk, where k is the wavevector and n is the refractive index of the gas in the measurement path. For the eleventh embodiment the measured value of L is not sensitive to translations of beam steering mirror 552 in a direction normal to its reflective surface, to first order in such translations.

The line of reference for the measurement beam of the tenth embodiment is defined by the direction of measurement beam 511, a defined zero orientation of beam-steering mirror 552, and the relationship between locations of polarizing beam splitter 558, mirror assembly 556, mirrors 554, 564A and 564B, and beam-steering mirror 552. For example, with beam-steering mirror 552 at the zero orientation and the projection of a spot, formed by beam 511 on beam-steering mirror 552, onto the opposite surface of 552 coinciding with the spot formed by beam 533, the corresponding path of beam 521 defines the line of reference when using φ₇ to determine the difference in physical path length.

The line of measurement is defined by the path of beam 521, when using φ₇ to determine the difference in physical path length, which intersects measurement object mirror 562 at normal incidence. The linear displacement represented by phase φ₇ is a displacement measured along the line of measurement. For the example given in the preceding paragraph, the line of measurement coincides with the line of reference and has a zero Abbé offset.

Alternatively, phase φ₈ can be used to determine a linear displacement in which case, the corresponding line of reference is parallel to the φ₇ line of reference but displaced by a distance a. The φ₈ line of measurement coincides with the path of beam 521 and has a nonzero Abbé offset a. Similarly, in other embodiments, the average of phases φ₇ and φ₈ can be used to calculate displacement L

Abbé offsets other than a can be incorporated into the eleventh embodiment by introducing a lateral displacement in the path of the measurement beam impinging on object mirror 562. The lateral displacement represents a parallel translation of a beam and can be produced by a rhomb prism such as rhomb 41 of the first embodiment.

The third embodiment of the second set of embodiments, the twelfth embodiment, comprises the interferometer system and beam-steering assembly of the seventh embodiment shown schematically in FIGS. 7a-7 c except that processor 682 (682H or 682HV) performs additional functions. For the twelfth embodiment, processor 682 further calculates the difference in physical path length L between the measurement and reference paths based on φ₁₀, i.e., L=φ₁₀/2nk, where k is the wavevector and n is the refractive index of the gas in the measurement path. For the twelfth embodiment the measured value of L is not sensitive to translations of beam steering mirror 652 in a direction normal to its reflective surface, to first order in such translations. Alternatively, in other embodiments, a separate distance measuring system can be included to process phase φ₁₀, so that the interferometric angle measurement for the servo signal is separate from the distance measurement.

The line of reference for the measurement beam of the twelfth embodiment is defined by the direction of measurement beam 611, a defined zero orientation of beam-steering mirror 652, and the relationship between locations of polarizing beam splitter 658, mirror assembly 656, mirrors 654, 664A and 664B, and beam-steering mirror 652. For example, with beam-steering mirror 652 at the zero orientation and the projection of a spot, formed by beam 611 on beam-steering mirror 652, onto the opposite surface of 652 coinciding with the spot formed by beam 633, the corresponding path of beam 621 defines the line of reference when using φ₁₀ to determine the difference in physical path length.

The line of measurement is defined by the path of beam 621, when using φ₁₀ line of reference, which intersects measurement object mirror 662 at normal incidence. The linear displacement represented by phase φ₁₀ is a displacement measured along the line of measurement. For the example given in the preceding paragraph, the line of measurement coincides with the line of reference and has a zero Abbé offset.

Abbé offsets can be incorporated into the twelfth embodiment by introducing a lateral displacement in the path of the measurement beam impinging on object mirror 662. The lateral displacement represents a parallel translation of a beam and can be produced by a rhomb prism such as rhomb 41 of the first embodiment.

In other embodiments similar to the tenth, eleventh, and twelfth embodiments described above, the interferometry system can measure angular displacements of the measurement object in two orthogonal planes and also measure a linear displacement of the measurement object. Three such embodiments respectively follow from the description of the variant of the second embodiment and the tenth embodiment described above, the description of the variant of the sixth embodiment (FIGS. 6c-g) and the eleventh embodiment described above, and the description of the variant of the seventh embodiment (FIGS. 7d-f) and the twelfth embodiment described above.

The fourth embodiment of the second set of embodiments, the thirteenth embodiment, comprises the interferometer system and beam-steering assembly of the eighth embodiment shown schematically in FIGS. 8a-c except that processor 790 performs additional functions. For the thirteenth embodiment, processor 790 further calculates the difference in physical path length L between the measurement and reference paths based on φ₁₃, i.e., L=φ₁₃/2nk, where k is the wavevector and n is the refractive index of the gas in the measurement path. For the thirteenth embodiment the measured value of L is not sensitive to translations of beam steering mirror 750 in a direction normal to its reflective surface, to first order in such translations. Alternatively, in other embodiments signal processor 790 calculates the linear displacement L from φ₁₄ or the average of φ₁₃ and φ₁₄. Furthermore, in other embodiments, the interferometry system can also measure angle along two orthogonal planes. The displacement measured by the twelfth embodiment can include Abbe offset considerations similar to those described above.

The angle and linear displacement calculations in the embodiments described above depend on the refractive index n_(M) of the gas in the measurement path. Changes in the refractive index, caused for example by air turbulence along the measurement path, can therefore alter the angle and displacement measurements. To compensate for such effects any of the interferometry systems described above can involve measurement and reference beams that include at least two separate wavelength components, e.g., dispersion interferometry. The reference and measurement beam components at each wavelength are combined with one another to form an overlapping pair of exit beams. Interferometric signals, e.g., phases φ_(i), at each wavelength are then derived from the respective overlapping pair of exit beams. Configuring interferometry systems such as those described above for measurements at multiple wavelengths is described in U.S patent application No. _____ entitled “Single-Pass and Multi-Pass Interferometry Systems Having a Dynamic Beam-Steering Assembly For Measuring Distance, Angle, and Dispersion” by Henry A. Hill and Peter de Groot, filed May 5, 1999 and having Attorney Docket No. 09712/036001, the contents of which is incorporated herein by reference.

In such embodiments, the processing systems and/or angle measuring systems in the embodiments described above will process respective phases φ_(i) at two or more wavelengths, in other words, the phases φ_(i) are now further indexed with respect to wavelength according to φ_(ij)=φ_(i)(λ_(j)), where λ_(j) specifies the wavelength of the particular component. Similarly, the terms η_(i) defined above with respect to one or more phases φ_(i)'s are now further indexed as η_(ij) to specify the wavelength λ_(j) of the phases φ_(i)'s. The processing systems and/or angle measuring systems then calculate the refractive effects of the gas on the angular displacement measurements as described below.

The description of the embodiments described herein noted that the angular orientations measured for the measurement object need to be corrected for the refractive effects of gas in a respective measurement path. The correction Δθ_(i), as given in the equations for θ_(i) of the second, third, fifth, sixth, seventh, and eighth embodiments, is expressed as $\begin{matrix} {{\Delta \quad \theta_{i}} = {- {\int_{i}{\left( \frac{\partial n}{\partial r}\quad \right){{s}.}}}}} & (23) \end{matrix}$

The correction Δθ_(i) can be rewritten to a good approximation in terms of a gradient of a dispersion and the reciprocal dispersive power Γ of the gas. The reciprocal dispersive power Γ is an intrinsic optical property of the gas and is defined as $\begin{matrix} {\Gamma = \frac{\left( {n_{l} - 1} \right)}{n_{q} - n_{u}}} & (24) \end{matrix}$

where l, q, and u are indices corresponding to wavelengths λ_(l), λ_(q), and λ_(u), respectively, q≠u, used in the dispersion interferometry. For a gas where there are no significant gradients in the composition of the gas in the measurement path, Eq. (23) and Eq. (24) can be combined to yield $\begin{matrix} {{{\Delta\theta}_{i} = {{- \Gamma}{\int_{i}{\left\lbrack \frac{\partial\left( {n_{q} - n_{u}} \right)}{\partial r} \right\rbrack \quad {s}}}}}{or}} & (25) \\ {{\Delta\theta}_{i} = {- {{\Gamma \left\lbrack {{\int_{i}{\left( \frac{\partial n_{q}}{\partial r} \right)\quad {s}}} - {\int_{i}{\left( \frac{\partial n_{u}}{\partial r} \right)\quad {s}}}} \right\rbrack}.}}} & (26) \end{matrix}$

The difference in the gradients of the refractivity are obtained from the difference in the measured θ_(i) at the respective wavelengths where the measured θ_(i) are uncorrected for refractive effects of the gas. In particular, the processing systems and/or angle measuring systems can calculate the correction according to Eq. (27) $\begin{matrix} {{\Delta\theta}_{i} = {{- 2}\Gamma \left\{ {{\arctan \left\lbrack \frac{\eta_{i\quad 1}}{1 + \eta_{i\quad 1}} \right\rbrack} - {\arctan \left\lbrack \frac{\eta_{i\quad 2}}{1 + \eta_{i\quad 2}} \right\rbrack}} \right\}}} & (27) \end{matrix}$

Note that corrections of the refractive effects of the gas on angular and linear displacement measurements both use the same intrinsic property of the gas, the reciprocal dispersive power Γ.

The interferometry systems described above can be especially useful in lithography applications that fabricate large-scale integrated circuits such as computer chips and the like. Lithography is the key technology driver for the semiconductor manufacturing industry. Overlay improvement is one of the five most difficult challenges down to and below 100 nm line widths (design rules), see for example the Semiconductor Industry Roadmap, p82 (1997). Overlay depends directly on the performance, i.e. accuracy and precision, of the distance measuring interferometers used to position the wafer and reticle (or mask) stages. Since a lithography tool may produce $50-100M/year of product, the economic value from improved performance distance measuring interferometers is substantial. Each 1% increase in yield of the lithography tool results in approximately $1M/year economic benefit to the integrated circuit manufacturer and substantial competitive advantage to the lithography tool vendor.

The function of a lithography tool is to direct spatially patterned radiation onto a photoresist-coated wafer. The process involves determining which location of the wafer is to receive the radiation (alignment) and applying the radiation to the photoresist at that location (exposure).

To properly position the wafer, the wafer includes alignment marks on the wafer that can be measured by dedicated sensors. The measured positions of the alignment marks define the location of the wafer within the tool. This information, along with a specification of the desired patterning of the wafer surface, guides the alignment of the wafer relative to the spatially patterned radiation. Based on such information, a translatable stage supporting the photoresist-coated wafer moves the wafer such that the radiation will expose the correct location of the wafer.

During exposure, a radiation source illuminates a patterned reticle, which scatters the radiation to produce the spatially patterned radiation. The reticle is also referred to as a mask, and these terms are used interchangeably below. In the case of reduction lithography, a reduction lens collects the scattered radiation and forms a reduced image of the reticle pattern. Alternatively, in the case of proximity printing, the scattered radiation propagates a small distance (typically on the order of microns) before contacting the wafer to produce a 1:1 image of the reticle pattern. The radiation initiates photo-chemical processes in the resist that convert the radiation pattern into a latent image within the resist.

The interferometry systems described above are important components of the positioning mechanisms that control the position of the wafer and reticle, and register the reticle image on the wafer.

In general, the lithography system, also referred to as an exposure system, typically includes an illumination system and a wafer positioning system. The illumination system includes a radiation source for providing radiation such as ultraviolet, visible, x-ray, electron, or ion radiation, and a reticle or mask for imparting the pattern to the radiation, thereby generating the spatially patterned radiation. In addition, for the case of reduction lithography, the illumination system can include a lens assembly for imaging the spatially patterned radiation onto the wafer. The imaged radiation exposes resist coated onto the wafer. The illumination system also includes a mask stage for supporting the mask and a positioning system for adjusting the position of the mask stage relative to the radiation directed through the mask. The wafer positioning system includes a wafer stage for supporting the wafer and a positioning system for adjusting the position of the wafer stage relative to the imaged radiation. Fabrication of integrated circuits can include multiple exposing steps. For a general reference on lithography, see, for example, J. R. Sheats and B. W. Smith, in Microlithography: Science and Technology (Marcel Dekker, Inc., New York, 1998), the contents of which is incorporated herein by reference.

The interferometry systems described above can be used to precisely measure the positions (e.g., distances and/or angular orientations) of each of the wafer stage and mask stage relative to other components of the exposure system, such as the lens assembly, radiation source, or support structure. In such cases, the interferometry system can be attached to a stationary structure and the measurement object attached to a movable element such as one of the mask and wafer stages. Alternatively, the situation can be reversed, with the interferometry system attached to a movable object and the measurement object attached to a stationary object.

More generally, the interferometry systems can be used to measure the position of any one component of the exposure system relative to any other component of the exposure system, in which the interferometry system is attached to, or supported by, one of the components and the measurement object is attached, or is supported by the other of the components.

An example of a lithography scanner 1400 using an interferometry system 1426 is shown in FIG. 9a. The interferometry system is used to precisely measure the position of a wafer within an exposure system. Here, stage 1422 is used to position the wafer relative to an exposure station. Scanner 1400 comprises a frame 1402, which carries other support structures and various components carried on those structures. An exposure base 1404 has mounted on top of it a lens housing 1406 atop of which is mounted a reticle or mask stage 1416, which is used to support a reticle or mask. A positioning system for positioning the mask relative to the exposure station is indicated schematically by element 1417. Positioning system 1417 can include, e.g., piezoelectric transducer elements and corresponding control electronics. Although, it is not included in this described embodiment, one or more of the interferometry systems described above can also be used to precisely measure the position of the mask stage as well as other moveable elements whose position must be accurately monitored in processes for fabricating lithographic structures (see supra Sheats and Smith Microlithography: Science and Technology).

Suspended below exposure base 1404 is a support base 1413 that carries wafer stage 1422. Stage 1422 includes a plane mirror 1428 for reflecting at least one measurement beam 1454 directed to the stage by interferometry system 1426. A positioning system for positioning stage 1422 relative to interferometry system 1426 is indicated schematically by element 1419. Positioning system 1419 can include, e.g., piezoelectric transducer elements and corresponding control electronics. The measurement beam(s) reflects back to the interferometry system, which is mounted on exposure base 1404. The interferometry system can be any of the embodiments described previously.

During operation, a radiation beam 1410, e.g., an ultraviolet (UV) beam from a UV laser (not shown), passes through a beam shaping optics assembly 1412 and travels downward after reflecting from mirror 1414. Thereafter, the radiation beam passes through a mask (not shown) carried by mask stage 1416. The mask (not shown) is imaged onto a wafer (not shown) on wafer stage 1422 via a lens assembly 1408 carried in a lens housing 1406. Base 1404 and the various components supported by it are isolated from environmental vibrations by a damping system depicted by spring 1420.

In other embodiments of the lithographic scanner, one or more of the interferometry systems described previously can be used to measure angles and/or distances along multiple axes associated for example with, but not limited to, the wafer and reticle (or mask) stages. Also, rather than a UV laser beam, other beams can be used to expose the wafer including, e.g., x-ray beams, electron beams, ion beams, and visible optical beams.

In addition, the lithographic scanner can include a column reference in which interferometry system 1426 directs the reference beam to lens housing 1406 or some other structure that directs the radiation beam rather than a reference path internal to the interferometry system. The interference signal produce by interferometry system 1426 when combining measurement beam 1454 reflected from stage 1422 and the reference beam reflected from lens housing 1406 indicates changes in the position of the stage relative to the radiation beam. Furthermore, in other embodiments the interferometry system 1426 can be positioned to measure changes in the position of reticle (or mask) stage 1416 or other movable components of the scanner system. Also, in other embodiments, the positions of interferometry system 1426 and plane mirror 1428 can be reversed, with the interferometry system on the movable stage and the plane mirror fixed to support structure. Finally, the interferometry systems can be used in a similar fashion with lithography systems involving steppers, in addition to, or rather than, scanners.

As is well known in the art, lithography is a critical part of manufacturing methods for making semiconducting devices. For example, U.S. Pat. No. 5,483,343 outlines steps for such manufacturing methods. These steps are described below with reference to FIGS. 9b and 9 c. FIG. 9b is a flow chart of the sequence of manufacturing a semiconductor device such as a semiconductor chip (e.g. IC or LSI), a liquid crystal panel or a CCD. Step 1451 is a design process for designing the circuit of a semiconductor device. Step 1452 is a process for manufacturing a mask on the basis of the circuit pattern design. Step 1453 is a process for manufacturing a wafer by using a material such as silicon.

Step 1454 is a wafer process which is called a pre-process wherein, by using the so prepared mask and wafer, circuits are formed on the wafer through lithography. Step 1455 is an assembling step, which is called a post-process wherein the wafer processed by step 1454 is formed into semiconductor chips. This step includes assembling (dicing and bonding) and packaging (chip sealing). Step 1456 is an inspection step wherein operability check, durability check and so on of the semiconductor devices produced by step 1455 are carried out. With these processes, semiconductor devices are finished and they are shipped (step 1457).

FIG. 9c is a flow chart showing details of the wafer process. Step 1461 is an oxidation process for oxidizing the surface of a wafer. Step 1462 is a CVD process for forming an insulating film on the wafer surface. Step 1463 is an electrode forming process for forming electrodes on the wafer by vapor deposition. Step 1464 is an ion implanting process for implanting ions to the wafer. Step 1465 is a resist process for applying a resist (photosensitive material) to the wafer. Step 1466 is an exposure process for printing, by exposure, the circuit pattern of the mask on the wafer through the exposure apparatus described above. Step 1467 is a developing process for developing the exposed wafer. Step 1468 is an etching process for removing portions other than the developed resist image. Step 1469 is a resist separation process for separating the resist material remaining on the wafer after being subjected to the etching process. By repeating these processes, circuit patterns are formed and superimposed on the wafer.

The interferometry systems described above can also be used in other applications in which the relative position of an object needs to be measured precisely. For example, in applications in which a write beam such as a laser, x-ray, ion, or electron beam, marks a pattern onto a substrate as either the substrate or beam moves, the interferometry systems can be used to measure the relative movement between the substrate and write beam.

As an example, a schematic of a beam writing system 1600 is shown in FIG. 10. A source 1610 generates a write beam 1612, and a beam focusing assembly 1614 directs the radiation beam to a substrate 1616 supported by a movable stage 1618. To determine the relative position of the stage, an interferometry system 1620 directs a reference beam 1622 to a mirror 1624 mounted on beam focusing assembly 1614 and a measurement beam 1626 to a mirror 1628 mounted on stage 1618. Interferometry system 1620 can be any of the interferometry systems described previously. Changes in the position measured by the interferometry system correspond to changes in the relative position of write beam 1612 on substrate 1616. Interferometry system 1620 sends a measurement signal 1632 to controller 1630 that is indicative of the relative position of write beam 1612 on substrate 1616. Controller 1630 sends an output signal 1634 to a base 1636 that supports and positions stage 1618. In addition, controller 1630 sends a signal 1638 to source 1610 to vary the intensity of, or block, write beam 1612 so that the write beam contacts the substrate with an intensity sufficient to cause photophysical or photochemical change only at selected positions of the substrate. Furthermore, in some embodiments, controller 1630 can cause beam focusing assembly 1614 to scan the write beam over a region of the substrate, e.g., using signal 1644. As a result, controller 1630 directs the other components of the system to pattern the substrate. The patterning is typically based on an electronic design pattern stored in the controller. In some applications the write beam patterns a resist coated on the susbstrate and in other applications the write beam directly patterns, e.g., etches, the substrate.

An important application of such a system is the fabrication of masks and reticles used in the lithography methods described previously. For example, to fabricate a lithography mask an electron beam can be used to pattern a chromium-coated glass substrate. In such cases where the write beam is an electron beam, the beam writing system encloses the electron beam path in a vacuum. Also, in cases where the write beam is, e.g., an electron or ion beam, the beam focusing assembly includes electric field generators such as quadrapole lenses for focusing and directing the charged particles onto the substrate under vacuum. In other cases where the write beam is a radiation beam, e.g., x-ray, UV, or visible radiation, the beam focusing assembly includes corresponding optics and for focusing and directing the radiation to the substrate.

Other aspects, advantages, and modifications are within the scope of the following claims. 

What is claimed is:
 1. An interferometry system comprising: an interferometer which during operation directs a measurement beam along a measurement path contacting a measurement object and combines each of at least two portions of the measurement beam with a corresponding reference beam to form at least two overlapping pairs of exit beams, the interferometer comprising a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the measurement beam to the measurement object, the measurement beam contacting the beam steering element; a control circuit which during operation causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object; and an angle measurement system which during operation calculates the change in angular orientation of the measurement object based on at least one of interferometric signals derived from the overlapping pairs of exit beams and the reorientation of the beam steering element.
 2. The interferometry system of claim 1, wherein during operation the angle measurement system calculates the change in angular orientation of the measurement object based on the reorientation of the beam steering element.
 3. The interferometry system of claim 1, wherein during operation the angle measurement system calculates the change in angular orientation of the measurement object based on the interferometric signals derived from the overlapping pairs of exit beams.
 4. The interferometry system of claim 1, wherein during operation the angle measurement system calculates the change in angular orientation of the measurement object along two dimensions.
 5. The interferometry system of claim 1, wherein during operation the angle measurement system further calculates changes in distance to the measurement object based on at least one of the interferometric signals derived from the overlapping pairs of exit beams.
 6. The interferometry system of claim 1, wherein during operation the control circuit generates a servo signal based on the interferometric signals derived from the overlapping pairs of exit beams and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 7. The interferometry system of claim 6, wherein during operation the control circuit causes the positioning system to reorient the beam steering element along two dimensions based on the servo signal.
 8. The system of claim 1, wherein the control circuit comprises a detector having spatially resolved detector elements operative to measure the position and/or direction of at least a portion of the overlapping pairs of exit beams, and wherein during operation the control signal generates a servo signal based on the measured position and/or direction and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 9. The system of claim 8, wherein the detector is operative to measure the difference in position and/or direction between the exit beams of at least one of the overlapping pairs of exit beams.
 10. The system of claim 8, wherein the detector is operative to measure the position and/or direction of the measurement beam component of at least one of the overlapping pairs of exit beams relative to a reference position and/or direction.
 11. The system of claim 1, wherein during operation the interferometer directs the at least two portions of the measurement beam to contact the beam steering element before combining each of them with the corresponding reference beam.
 12. The system of claim 1, wherein during operation the control circuit causes the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.
 13. An interferometry system comprising: an interferometer which during operation directs a measurement beam along a measurement path contacting a measurement object, separates the measurement beam into m portions, and recombines at least a part of one of the portions with each of the remaining m−1 portions to form m−1 overlapping pairs of exit beams, the interferometer comprising a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the measurement beam to the measurement object and receive the m separated portions, the measurement beam and each of the m separated portions contacting the beam steering element; a control circuit which during operation causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object; and an angle measurement system which during operation calculates the change in angular orientation of the measurement object based on at least one of interferometric signals derived from the m−1 overlapping pairs of exit beams and the reorientation of the beam steering element.
 14. The interferometry system of claim 13, wherein m is one of 2 and
 3. 15. The interferometry system of claim 13, wherein during operation the angle measurement system calculates the change in angular orientation of the measurement object along two dimensions.
 16. The interferometry system of claim 13, wherein during operation the control circuit generates a servo signal based on the interferometric signals derived from the m−1 overlapping pairs of exit beams and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 17. The system of claim 13, wherein the control circuit comprises a detector having spatially resolved detector elements operative to measure the position and/or direction of at least a portion of the m−1 overlapping pairs of exit beams, and wherein during operation the control signal generates a servo signal based on the measured position and/or direction and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 18. The system of claim 13, wherein during operation the control circuit causes the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.
 19. An interferometry system comprising: an interferometer which during operation directs two measurement beams along corresponding measurement paths contacting a measurement object and combines the measurement beam to form an overlapping pair of exit beams, the interferometer comprising a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the two measurement beams to the measurement object, the two measurement beams contacting the beam steering element; a control circuit which during operation causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object; and an angle measurement system which during operation calculates the change in angular orientation of the measurement object based on at least one of an interferometric signal derived from the overlapping pair of exit beams and the reorientation of the beam steering element.
 20. The interferometry system of claim 19, wherein during operation the control circuit generates a servo signal based on the interferometric signal derived from the overlapping pair of exit beams and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 21. The system of claim 19, wherein the control circuit comprises a detector having spatially resolved detector elements operative to measure the position and/or direction of at least a portion of the overlapping pair of exit beams, and wherein during operation the control signal generates a servo signal based on the measured position and/or direction and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 22. The system of claim 19, wherein during operation the control circuit causes the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.
 23. The system of claim 19, wherein the interferometer directs the two measurement beams to contact the measurement object at substantially the same location.
 24. An interferometry system comprising: an interferometer which during operation receives an input beam, splits the input beam into a measurement beam and m reference beams, where m is an integer greater than 1, directs the measurement beam along a measurement path contacting a measurement object, separates the measurement beam into m portions, and combines each of the m portions of the measurement beam with a corresponding one of the m reference beams to form m overlapping pairs of exit beams, a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the input beam and the m overlapping pairs of exit beams, the input beam and the m overlapping pairs of exit beams contacting the beam steering element; a control circuit which during operation causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object; and an angle measurement system which during operation calculates the change in angular orientation of the measurement object based on at least one of interferometric signals derived from the m overlapping pairs of exit beams and the reorientation of the beam steering element.
 25. The interferometry system of claim 24, wherein during operation the angle measurement system further calculates changes in distance to the measurement object based on at least one of the interferometric signals derived from the m overlapping pairs of exit beams.
 26. The interferometry system of claim 24, wherein during operation the control circuit generates a servo signal based on the interferometric signals derived from the overlapping pairs of exit beams and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 27. The system of claim 24, wherein the control circuit comprises a detector having spatially resolved detector elements operative to measure the position and/or direction of at least a portion of the overlapping pairs of exit beams, and wherein during operation the control signal generates a servo signal based on the measured position and/or direction and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 28. The system of claim 24, wherein during operation the control circuit causes the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.
 29. An interferometry system comprising: an interferometer which during operation receives an input beam, splits the input beam into two measurement beams, directs the measurement beams along respective measurement paths contacting the measurement object, and combines the measurement beams to form an overlapping pair of exit beams, a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the input beam and the overlapping pair of exit beams, the input beam and the overlapping pair of exit beams contacting the beam steering element; a control circuit which during operation causes the 0positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object; and an angle measurement system which during operation calculates the change in angular orientation of the measurement object based on at least one of an interferometric signal derived from the overlapping pair of exit beams and the reorientation of the beam steering element.
 30. The interferometry system of claim 29, wherein during operation the control circuit generates a servo signal based on the interferometric signal derived from the overlapping pair of exit beams and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 31. The system of claim 29, wherein the control circuit comprises a detector having spatially resolved detector elements operative to measure the position and/or direction of at least a portion of the overlapping pair of exit beams, and wherein during operation the control signal generates a servo signal based on the measured position and/or direction and causes the positioning system to reorient the beam steering element in response to the change in angular orientation of the measurement object based on the servo signal.
 32. The system of claim 29, wherein during operation the control circuit causes the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.
 33. An interferometry system comprising: an interferometer which during operation directs a measurement beam along a measurement path contacting a measurement object, separates the measurement beam into first and second portions, directs the first and second portions along separate paths, and subsequently recombines the first and second portions with each other to form at least one overlapping pair of exit beams, the interferometer comprising a beam steering assembly having a beam steering element and a positioning system to orient the beam steering element, the beam steering element positioned to direct the measurement beam to the measurement object and subsequently receive the measurement beam from the measurement object, the measurement beam thereby twice contacting the beam steering element, after which the interferometer separates the measurement beam into the first and second portions; a control circuit which during operation causes the positioning system to reorient the beam steering element in response to a change in angular orientation of the measurement object based on at least one interferometric signal derived from the at least one overlapping pair of exit beams; and an angle measurement system which during operation calculates the change in angular orientation of the measurement object based on the reorientation of the beam steering element.
 34. The interferometry system of claim 33, wherein the interferometer recombines the first and second portions into two overlapping pairs of exit beams, and the at least one interferometric signal is at least two interferometric signals derived from the two overlapping pairs of exit beams.
 35. The interferometry system of claim 34, wherein the control circuit comprises two detection channels which during operation measure the at least two interferometric signals, one of the detection channels comprising a quarter wave plate oriented to cause the two interferometric signals to be in quadrature with one another.
 36. The interferometry system of claim 33, wherein during operation the interferometer further separates the measurement beam into third and fourth portions after the measurement beam twice contacts the beam steering element, directs the third and fourth portions along separate paths, and recombines the third and fourth portions to form a second at least one pair of overlapping exit beams, and wherein during operation the control circuit causes the positioning system to reorient the beam steering element along two dimensions based on the at least one interferometric signal and a second at least one interferometric signal derived from the second at least pair of overlapping exit beams.
 37. The interferometry system of claim 33, wherein during operation the angle measurement system calculates the change in angular orientation of the measurement object along two dimensions.
 38. The interferometry system of claim 33, wherein the during operation the interferometer further separates the measurement beam into an additional portion after the measurement beam twice contacts the beam steering element and combines the additional portion with a reference beam to form an additional pair of overlapping exit beams, and wherein the interferometry system further comprises a distance measurement system which during operation measures changes in distance to the measurement object based on an interferometric signal derived from the additional pair of overlapping exit beams.
 39. The interferometry system of claim 1, wherein the interferometer further comprises a plurality of reflective surfaces oriented to direct the measurement beam, the portions of the measurement beam, a progenitor beam for the reference beams, and the reference beams, and for initial linear polarizations and propagation directions for the measurement beam and the progenitor beam, the plurality of reflective surfaces is oriented to preserve a linear polarization for the measurement beam, the portions of the measurement beam, a progenitor beam for the reference beams, and the reference beams upon their successive reflections.
 40. The interferometry system of claim 13, wherein the interferometer further comprises a plurality of reflective surfaces oriented to direct the measurement beam and the portions of the measurement beam, and for an initial linear polarization and propagation direction for the measurement beam, the plurality of reflective surfaces is oriented to preserve a linear polarization for the measurement beam and the portions of the measurement beam upon their successive reflections.
 41. The interferometry system of claim 19, wherein the interferometer further comprises a plurality of reflective surfaces oriented to direct the measurement beams, and for an initial linear polarization and propagation direction for a progenitor beam for the measurement beams, the plurality of reflective surfaces is oriented to preserve a linear polarization for the measurement beams upon their successive reflections.
 42. The interferometry system of claim 24, wherein the interferometer further comprises a plurality of reflective surfaces oriented to direct the measurement beam and the reference beams, and for an initial linear polarization and propagation direction for the input beam, the plurality of reflective surfaces is oriented to preserve a linear polarization for the measurement beam and the reference beams upon their successive reflections.
 43. The interferometry system of claim 29, wherein the interferometer further comprises a plurality of reflective surfaces oriented to direct the measurement beams, and for an initial linear polarization and propagation direction for the input beam, the plurality of reflective surfaces is oriented to preserve a linear polarization for the measurement beams upon their successive reflections.
 44. The interferometry system of claim 33, wherein the interferometer further comprises a plurality of reflective surfaces oriented to direct the measurement beam and the portions of the measurement beam, and for an initial linear polarization and propagation direction for the measurement beam, the plurality of reflective surfaces is oriented to preserve a linear polarization for the measurement beam and the portions of the measurement beam upon their successive reflections.
 45. An interferometry method comprising: directing a measurement beam along a measurement path contacting a measurement object; combining at least a portion of the measurement beam with another beam to form an overlapping pair of exit beams; using an electronic control system to redirect the measurement beam in response to a change in the angular orientation of the measurement object based on a servo signal derived from at least a portion of the overlapping pair of exit beams; and calculating the change in angular orientation based on at least one of an interferometric signal derived from the overlapping pair of exit beams and the redirection of the measurement object.
 46. The interferometry method of claim 45 wherein using the electronic control system comprises redirecting the measurement beam to contact the measurement object at substantially normal incidence over a range of angular orientations of the measurement object.
 47. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 1 secured to the second component, wherein the measurement object is a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 48. The lithography system of claim 47, wherein the second components is a movable stage which during operation supports a wafer.
 49. The lithography system of claim 47, wherein during operation the beam steering element causes the measurement beam to contact the mirror at substantially normal incidence over a range of angular orientations of the measurement object.
 50. A lithography method comprising: positioning a first component of a lithography system relative to a second component of a lithography system to expose a wafer to spatially patterned radiation; and measuring the position of the first component relative to the second component using the method of claim 45 wherein the first component includes the measurement object.
 51. A beam writing system for use in fabricating a lithography mask, the system comprising: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and the inteferometry system of claim 1 for measuring the position of the stage relative to the beam directing assembly.
 52. A beam writing method for use in fabricating a lithography mask, the method comprising: directing a write beam to a substrate to pattern the susbtrate; positioning the substrate relative to the write beam; and measuring the position of the substrate relative to the write beam using the interferometry method of claim
 45. 53. The lithography system of claim 47, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 54. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 13 secured to the second component, wherein the measurement object is a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 55. The lithography system of claim 54, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 56. The lithography system of claim 54, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 57. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 19 secured to the second component, wherein the measurement object is a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 58. The lithography system of claim 57, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 59. The lithography system of claim 57, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 60. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 19 secured to the second component, wherein the measurement object is a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 61. The lithography system of claim 60, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 62. The lithography system of claim 60, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 63. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 24 secured to the second component, wherein the measurement object is a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 64. The lithography system of claim 63, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 65. The lithography system of claim 63, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 66. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 29 secured to the second component, wherein the measurement object is a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 67. The lithography system of claim 66, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 68. The lithography system of claim 66, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 69. A lithography system for fabricating integrated circuits comprising: first and second components, the first and second components being movable relative to one another; and the interferometry system of claim 33 secured to the second component, wherein the measurement object i a mirror rigidly secured to the first component and during operation the interferometry system measures the position of the first component relative to the second component.
 70. The lithography system of claim 69, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 71. The lithography system of claim 69, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 72. The lithography method of claim 50, wherein one of the first and second components is a movable stage which during operation supports a wafer.
 73. The lithography system of claim 50, wherein one of the first and second components is a reticle for filtering radiation used to illuminate a wafer.
 74. A beam writing system for use in fabricating a lithography mask, the system comprising: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and the inteferometry system of claim 13 for measuring the position of the stage relative to the beam directing assembly.
 75. A beam writing system for use in fabricating a lithography mask, the system comprising: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and the inteferometry system of claim 19 for measuring the position of the stage relative to the beam directing assembly.
 76. A beam writing system for use in fabricating a lithography mask, the system comprising: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and the inteferometry system of claim 24 for measuring the position of the stage relative to the beam directing assembly.
 77. A beam writing system for use in fabricating a lithography mask, the system comprising: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and the inteferometry system of claim 29 for measuring the position of the stage relative to the beam directing assembly.
 78. A beam writing system for use in fabricating a lithography mask, the system comprising: a source providing a write beam to pattern a substrate; a stage supporting the substrate; a beam directing assembly for delivering the write beam to the substrate; a positioning system for positioning the stage and beam directing assembly relative one another; and the inteferometry system of claim 33 for measuring the position of the stage relative to the beam directing assembly. 